There is a lot of misunderstanding about the resources he himself owns and how to use them.
One important thing to be taken into account is the "Aspect Ratio"... trying to stretch a 4:3 image into a 16:9 only make your characters fatty
If wanting a coherent image for the game, try and find a 16:9 patch for it, supposing that game does not have original widescreen native support.
Second, the Internal resolution has not much to do with the screen resolution (this last is set at the Window GS). If I recall correctly PCSX2 uses a borderless windowed mode for full screen which have some advantages and making less dangerous the fallback to desktop and returning to the game.
So, the original PS2 resolutions are variable among games and even for a same game and made in a way that makes hard to upscale without those glitches. Finding a correct relation to that "internal" resolution may reduce considerable the glitches or eliminate it totally.
So, there are a lot more concepts about image and it's representation in digital media that seems at first and blindly tweaking it is not the best action. For sure is advantageous keeping the "external resolution" equal your monitor native resolution even if keeping the aspect ratio (to reduce the GPU driver rescaling)... just remember this is valid only for real full screen for any window will keep what is defined by the videocard driver as "desktop" resolution... commonly it being the monitor's native resolution.
PS: "Oddly" is this same background work from the drivers which exposes "defects", pixelation, jaggedness... that the TV would mask and make it soft.