If you're a beginner etcher and you happen to run into any of these issues, here are the solutions I've found!
Paper is completely rippled and folded after run through the press
Take off the tape on the backside. When it gets warm, it shifts and so does the plate under the press roller, thus causing this issue.
Print becomes weaker with heavier paper
This whole thing may also depend on the press and felts, but for me it seemed to have to do with the weight and the percentage of cotton in the paper. The heavy printmaking papers I've tried were 100% cotton, and I had terrible results. I then tried a 200 g/sm watercolour paper that had 50% cotton, then one with 25% cotton and the same weight. The latter yielded the best results for me so far. I've had this issue with two very different presses, so I can imagine this happening with others as well. Different soaking times and pressures had no effect on this.
[Edinburgh etch for zinc] Aquatints show irregular, wave-like patterns
Don't add dishwashing liquid. It's amazing for dealing with the bubbles when you etch lines (so they don't become dotty), but will also cause irregular aquatint biting. Consider having two acid tanks, a weaker one for aquatints and a strong one for lines that can have washing up liquid in it.
White stripe pattern on the plate
Caused by degreasing fluid drying on the plate. It doesn't always print, but sometimes it annoyingly does. I've stopped degreasing my plates and instead thoroughly wipe them with white spirits before aquatints and hard grounds. My old asphalt based hard ground would still crumble off the plate, but it often did that even on a properly degreased plate.