Look, there is no need to panic, I am a fan from Pakistan of Resident Evil 2 and had the same glitches as you have. Firstly, check in the gfxsetup.exe if you have set your 3D card to Unknown and keep it on high graphic priority. Then, set your resolution at 640 x 480 at the full screen, try both the 640 x 480 options, which ever runs faster.
Secondly, install compatibilty tool 5.0, just google it and you will get a link to download it (Dont worry, its from microsoft itself). You need a good internet connection for this as the setup requires several items that need to be downloaded during and after setup, follow it and download them and install them too. Once all is done, go to start menu and run "standard user analyzer" present in the menu of the compatibility tool. On screen, you can see a browse button, click it and choose leonp.exe or clairep.exe (which ever you want)and click launch, all the glitches should be removed by now.
The only problem I encountered even after all this is that the game is not that fast as it runs in Win98, but the speed is decent enough and will not jerk. Also, the windowed mode runs faster but the movies lose their video(only sounds are heard during a movie), and sometimes the smaller videos like spade key movie or chest open for king plug or blue stone movie is skipped (but as yet, no movie has skipped that features any sort of entry of claire or leon)
