I keep running into this Assertion error ("An Assertion failed in D:\Dev\Baldur\CVisibility.cpp at line number 1484") in Candlekeep. I had just defeated an enemy at a house. Then I tried to enter another building and this error popped up. I tried clearing the Baldur's Gate cache, but the folder was already empty. I only have the widescreen and GUI mods installed from the GOG forum. Is there a way to fix this Assertion issue?

Given your recent problem regarding the widescreen mod (ie. you are using it), this issue is almost certainly to do with that mod. If you use the WS mod in BG1, you cannot, under any circumstances, change resolution or use a saved game from a session in a different resolution from that set by the WS mod. This mod is a pain in the backside for BG1 users for that reason. There is an option, when installing the mod, to convert saved games to the current resolution, but it is NOT foolproof. The crux of the matter is, use the WS mod in BG1 at your own risk.

If there are issues with the gibberlings3 WS mod, is there an alternative way to make the resolution higher than 640x480 with just BG1?

Not with vanilla BG1, no. There is a way, if you don't mind playing BG1 in the BG2 engine, but be aware that this makes the game overpowered, because you will have spells, powers, weapons etc. from BG2 in BG1. There are two options:
1. EasyTuTu
2. BGT

The differences between them are EasyTuTu is BG1 only in the BG2 engine, and is self-contained, allowing you to play BG2 vanilla. BGT, on the other hand, combines the entire trilogy (from Candlekeep right through to Throne of Bhaal) into one game, seamlessly transferring your character, and other key characters with all of their stats from BG1 to 2, to ToB. But you will not be able to play BG2 vanilla.

Important: BGT must be installed with a completely clean BG1 installation (no patches, mods or overrides of any kind).

That's too bad that both mods require the 2nd game, as I only have the first one. But hopefully the info in this thread will help other people get BG1 to run in a higher resolution.