Just tried what you said in Mario, and it indeed fixes all the problems

Nice one, and a great first post!
Emulating HW T&L caps using 3D Analyze 2.13 also makes the errors go away in Mario.
Also tried this with Banjo Kazooie which works at a fast frame rate but suffers from slight stutter (even with Limit FPS and Sync game to audio)
MarioKart64 works fine also and looks really good. However when the Kart turns the screen 'stutters' the framerate is unaffected but it renders the game unplayable.
Off to test again now
1964 latest version results
Mario Kart works perfectly, frame rate is excellent, no stutter either
Banjo Kazooie again works perfectly it would seem
Mario works perfectly also