What were you doing at the time, what were the AI's doing at the time, where you shooting it out, was an ability being used, were you clicking on a planet, etc....  Assert messages aren't very helpful unless you know what's going on and then you have probable causes for it to look at.

The mesh error might be caused by you removing the weapons from the entity file, but not the weapon points from the mesh file.

Conversely, if you have weapons in the entity file and no points in the mesh they fire from the center and give you an error stating something like CAPITALSHIP_TECHCARRIER has weapon:2 damage in BACK bank but no weapon points

If the 4th faction is crashing when you're playing it and not when the AI plays it, then there's definitely something wrong with it.  Probably something that you're activating that the AI doesn't.  To check, just build one of everything, ships structures, planet upgrades...  Then select each thing individually and select all of it's options one at a time.  From experience whatever you last clicked on before the game crashed is the most likely offender since you're forcing the engine to work with that ship/structure/buff/ability.  However!

Something to consider is if you're playing Diplomacy with your graphics being up too high.  Sins is only a 32bit program so it's only allowed to use 2Gigs of RAM, high graphics selections tends to make the game crash 5 to 10 minutes in depending on how quickly everyone builds up.  Adding a 4th faction is sure to get you there faster then just modding the originals.  So if you haven't done that, do it before you do anything else and you'll see the crashing time extends to much longer in between or stops all together.  Even at not so high settings, you've added a lot of resources to get preloaded so maybe try out your testing with the settings on low and skyboxes and bloom turned off.  Basically do whatever you can to help your system not hit the wall, especially while testing.

As for the weapon points, if your entity files are only saying there's one weapon and your meshes are showing points for unused types, especially for some where there's 11 and 12 points for a weapon, then yes, that's a problem because you've got references to things that don't exist.  If the engine can't find a file, it'll search and search and search, and never give up giving you a memory leak until you hit the limit and crash.  If it's got references to things that don't exist, it slows down trying to figure out where they are.  So whenever you change something, you want to change every reference to your original change as well no matter what file they're in.  Aside from reducing the leaks, you have files that are cleaner better prepared for future changes.

Yeah, you really should have updated your game to 1.051 before jumping into it.  Might have saved you from some of the issues.  There really aren't very many changes between entrenchment and diplomacy though.  The big gap was between vanilla and entrenchment.  Everything you've already done can carry over without issue for the most part.  Diplomacy however has it's own little quirks like hitting the 2gig limit fairly quickly if your settings are on highest.  Naturally the easiest thing to do is turn the settings down and caution people playing to do the same, but results tend to vary.

Best advice I can give you is go slowly.  The less you do between testing runs, the easier it will be to find your mistake when you start getting errors.