ZD, you should do some research before you post random facts. Your post is riddled with errors.
1) Offspring of a mamzer or mamzeres are mamzerim. The offspring of most other arayos are also mamzeirim. Although this is not relevant to the discussion, what you wrote is factually incorrect.
2) False geirus could lead to mamzeirus, or false mamzeirim.. It might not happen often, but if a woman married a false ger and left without a get, and remarried, her children from her new husband would be wrongly considered mamzeirim. If she then left him without a get, and her first husband died, she would be considered a widow, when in reality she’s an eshes ish, and any children from a third husband would be unknown mamzeirim.
3) The discussion wasn’t even about mamzeirus. Intermarriage is a tragedy even if the children are kosher.
4) You can’t extrapolate what Rav Moshe would have held about some of these conversions. The circumstances are completely different. He dealt with Orthodox rabbis. Weiss considers himself Orthodox, but he’s not.
5) A kohen may not marry or stay married to a giyores. The kesuba is not valid because we want him to divorce her and not dissuaded by financial considerations. The children are indeed challalim. You got that part right.
Also, I don’t know what you mean “there are no standard conversions”. There is a Shulchan Aruch. There are some things which are a machlokes, but you want to throw the whole thing out!