Inconsistencies pop up during writing and role playing. Really, writing and role playing can be considered two sides of the same coin and when doing fan-fic and role playing with already created and codified stories that have their own canon, conflicts will happen!
For those unfamiliar with this term, please visit here on Wikipedia for a very good explanation. Generally try not to use Hammerspace, it is going to come up from time to time though. Video games make extensive use of this concept, guns, ladders, ropes, hoses, even people coming out of nowhere, where they would never fit. Role players in games like Dungeons and Dragons often ignore encumbrance rules in actual play and carry around 100's of 1000's of pounds of crap on their back like it's nothing. In fantasy settings this is often taken care of by a portable hole or bag of holding. In one game in particular Star Trek Voyager Elite Force this is taken care of by the use of a kind of infinitely powered transporter pattern buffer. Indeed the major plot point for Doctor Who where the TARDIS is bigger on the inside comes into play here too. So it isn't like it isn't possible, there is even an entire episode of Doctor Who where they make extensive jokes about dimensions bending and the TARDIS being smaller and smaller on the outside to the point that the Doctor cannot even get out of it.
Whatever the mechanism Hammerspace should be kept in the background unless for some amount of comic relief, too much reliance on this idea can trigger someone to actually ask a player to codify how they fit so much of something inside such a limited space of something else.
When two universes which are incompatible in ways meld together, inevitably there will be a conflict of ideas and technologies which are integral to both settings. This is also dealt with using "the Fudge". For example, differences like this come into play when one universe says "it is not possible to do..." and then another universe says the exact opposite. In most cases this is fixed by saying a character from universe A cannot do, whatever it is, but the character from universe B can. Some in game explanation can be given for why but it is not required. In areas of magic, technology, or the like it is generally understood that a player can decide to adopt technology or be taught how to do something previously impossible but this idea should be taken with a grain of salt.
Can / Can't of Technology
Technology can be passed around. So if some universe, lets call it Alpha, says that like beam weapons are impossible. This means that they cannot have lasers, phasers, etc... Then another universe called Zeta comes along, where beam weapons are widely used. Most of the time it is best to say that a character from Alpha won't trust or won't really know how to use a beam weapon from Zeta. It's possible, but generally we discourage it unless a reason for the discrepancy can be created of why Alpha says it isn't possible.
Can / Can't of the Supernatural
Supernatural forces work differently. Say we have the same two universes, Alpha and Zeta. In Zeta they know that Magic does not exist but in Alpha it does. What does one do? Would magic be ineffective on the character from Zeta? Can Zeta people learn to use Magic? No, it would not be ineffective and no they cannot. Magical or supernatural forces should be kept rather clear of each other. That is to say, a character from Alpha can be a majorly powerful mage to sling magic around like it is nothing. But the Zeta character cannot learn to do this, it goes against everything he or she has ever known, it just cannot happen.
Supernatural and Technological
The question them comes up where you have a magical character from Alpha and a technological character from Zeta get together. Can the Zeta one explain how to do technological craziness to the Alpha one? No. Because such things go completely against what those characters have ever known, their very ideas of how the universe works. No. There is some room for fudging this too, of course, but in general the answer would be no.
When doing dice-based role playing usually there is a book the codifies how everything works and a game master can decide how to bring in elements from other books. This kind of direct translation is an easy way to bring in opposing elements. This is what has been done here with such things as the Falcon Class Starship which is, of course, the YT-1300 cargo ship from Star Wars. There is no real way to say this isn't borrowed from Star Wars, so don't bother. In some areas this sites puts a hat on thing. By that, I mean it is noted that the design was based on... Insert origin of the idea here. This allows a writer to take the idea, reshape it in an entirely new way that works for the story being done, and use it.
As with the 2009 Star Trek reboot, if a person wants to completely re-do something in their own way the creation of an alternate timeline can be used. This creates an entirely new version which can be shaped, reshaped, and altered to suit specific purposes, which is what is done here with ideas from Stargate. It was impossible to reconcile most of the story elements of the Stargate franchise with Star Trek which is largely the canvas that Solas Tempus is painted in. So, while it hasn't been explicitly said, an alternate timeline is created where we can make it work.
This kind of taking an idea and reworking it lacks a certain amount of credibility, and when using it, a person should be aware of this.
Most of Solas Tempus takes place in the 24th century which interludes into other times. It is also noted that there is a multiverse with infinite realities. In a Doctor Who crossover with Star Trek done by IDW Publishing they created a reason for two alternate realities that would normally be incompatible to reside with each other so that The Doctor could appear on the Enterprise. They also made a big deal about putting a hat on the fact that these two universes were incompatible and leaving them merged would cause serious problems. This is a great way to handle temporary bridges between different storylines. Two realities, merged by some event, and then the game or story goes into writing things to the way they should be.
That isn't the only way to do things, however.
More Similar Than Different
Magic and magical items have been introduced to Solas Tempus, originally with the Solar Crystal. Other items were introduced as well which fall under the 24th century care of Vident Obscura which studies the unexplained. This creates an architecture in Solas Tempus for describing items as magical and having incredible abilities which are not covered by science, even within the nearly limitless bounds of what can be done with Star Trek.
A magic item from Angelic Sins can be used in both story lines because Angelic Sins takes place almost entirely in the 20th and 21st centuries. Solas Tempus takes place in the 24th century so it is conceivable that (since we adhere to the idea of the multiverse) the same item, with the same properties, and at least similar history can exist in both places without too much trouble. Since the two settings done directly conflict, someone wanting to use a magical item can look at the description of the item and toss out the bits which don't make sense. A good magical item description on the wiki should be made in such a way to allow the item to be used in different settings, if possible.
Someone looking at an entry that lists a history going from the 19th to the 24th centuries need not worry about anything beyond the time period they are playing in. Similarly, a person could make a note about a split in the history of an item, place, or some such which dictates the differences in between two universes leaving the rest of the entry the same.
The term of put a hat on it comes from the idea that the writer lets the audience know that they realize something is overly convenient, strange, or somehow obviously a tool. This idea breaks the 4th wall but lets the audience know the writer is aware something has been fudged or otherwise resolved in an obviously unskilled way. Letting the audience know that the writer is aware something, perhaps, might have been done better with more work or just doesn't mesh very smoothly can allow the audience to move past a glaring issue and enjoy the rest of the plot. At the very least the writer doesn't come off as being unaware that some of the writing could perhaps use improvement, more work, or was just plainly difficult to accept.
Try to make things work out, make sense, and mesh well. But don't sweat the details if you don't have to. Have fun with it, put a hat on it. I like hats.