I decided to play through TW3 again the other day and updated before doing so. I updated from 1.07, which I recall as being stable. Anyway, after updating I started a "new game+" game and begane playing only to find that I get a lot of freezes, both during and out of cutscenes. I'm also seeing weird mesh/texture glicthes.

NPCs will either have their meshes tear across the screen from the center of their torso or their torsos will become un-rendered/transparent. I had issues like this with 1.07 but not to this extent and only in White Orchard.

Is this common with 1.3 and, if so, is there a previous patch I'd be better off with (Since I obviously can't go back to 1.07 lol)?

Reinstall the full game, runs very smooth after it. I did the same. Update can trash your Witcher Folder. Clean install would take out the mess:)

To the OP: ^^ This.

Do NOT update from 1.07. Uninstall the game completely, from Control Panel. Re-download and install from the new installers.

Installing from disc is okay too or does it have to be the download? I really don't want to use _that_ much bandwidth.

No, do not install from disk. Those installers are just too old. You need to download the 1.10 installer and all the updates, unless you want to wait for the all-in-one that GOG is working on, but they say it will take "some time", because of the sheer size of the game.