I don't have a screenshot to show, but I was wondering if anyone else has the same problem. It happens quite frequently, but it's not a game-breaking deal, just extremely irritating. For example, sometimes the sprites of my lasers suddenly change to a different texture. And more frequently, when ships enter sub-space, and the blue, round sub-space sprite comes up, it often glitches, showing other textures for a split second
I'll try to get a screenshot later. Anyway if it's of any help, I'm using dgVoodoo, because the native game refuses to run without lagging like crazy

Do you really need the Glide wrapper? If you are having performance issues and you are using an Nvidia card, then you should check the fix in this thread The default game runs fine for me using that fix without a Glide wrapper and it has never had the glitches you describe. The Glide wrapper could actually be causing those glitches.
Alternatively, get FreeSpaceOpen and FSPort, you won't have this issue at all and you'll be able to play it at much higher resolutions and graphical quality.

I've tried that before, it didn't work, so I had to resort to using a wrapper
Anyway I decided to bite, and try out FSOpen. I avoided it before because it was all very confusing. I don't want to play FS2 yet, I want to finish FS1 and Silent Threat, since it's been 10 years when I last played, and I'd like to catch up on the first 2 games again. However, the wiki doesn't seem to cover much about getting FS1 to work on FSOpen.
Right now I'm downloading Freespace 2 just in case FSOpen needs FS2 in order for FS1 to run. It just seems so overwhelmingly difficult to set up. I don't even know if FSPort is a separate project from FSOpen lol - just goes to show how confused I am about this set up. So, some questions:
1) Is FSOpen related to FSPort? Do I need FSPort downloaded to run FS1 on FSOpen?
2) Do I need to copy all my FS1 files into my FSOpen install directory?
3) Do I need FS2 downloaded to play FS1 on FSOpen?
I have more questions, but my head's spinning from TMI right now lol

How do I get FS1 working in FSOpen, if I don't want to use FSPort?

You don't.

Alright I see what you mean, after trying out FSOpen. It's way less trouble than I'd imagined it to be lol. Thanks.
-edit-
By the way, are all the cutscenes from Freespace 1 in FSPort? And is there any way I can port my save games from Freespace 1 over to FSPort?

The cutscenes are available for FSPort. If you have a file called FS1OGGcutscenepack.vp in your \freespace2\fsport\ folder, you have them already. If not, they can be downloaded from the FSPort release thread at Hard Light Productions (http://www.hard-light.net/forums/index.php/topic,58357.0.html).
Unfortunately I think that the pilot files created and used by FS1 are different from the FS2 pilot files and you cannot use them.

Nice. Many thanks!