A lot of graphical issues can be caught with the GE debugger. Finding them gives a good picture of what's wrong, which makes it a lot easier to try and fix the issue.
Some issues, like the screen showing entirely black, may not be graphical issues and only appear to be. This method only helps find issues that are rendering related. It also only works on Windows (or WINE), currently.
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Find the issue. Get where you can see it or create a savestate right before it happens.
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Open the GE Debugger. Go to Debug -> GE Debugger.
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Click "Step Frame" to stop at the start of the next frame.
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Click "Step Prim" until you see the area that is being drawn improperly highlighted in red. Make sure ONLY the wrong area is red - if the entire screen is red, it's keep hitting Step Prim.
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If that takes too long, you can click "Step Tex" or "Step Draw" to go faster. But, you eventually need to click "Step Prim" and have it highlight the area that has the problem. If you pass it with "Step Tex", you'll have to start over from "Step Frame".
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Copy (screenshot is fine, Ctrl-C also works) each of the tabs in the GE debugger. It's a good idea to resize the height tall as possible if doing screenshots. Especially important are Settings and Texture. A screenshot of the previews at the top is also helpful (the left one is the current texture.)
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Post these in a bug. You can drag and drop into GitHub issues to upload, or put them on some external site (https://gist.github.com/ is highly recommended), up to you.
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It's a good idea to click "Step Draw" to double check that what you found was actually drawn incorrectly (in case it is instead drawn on top of later, incorrectly - if it is, you need the log info from that.)