That's a major problem. Anything that could possibly be caused by the vaccine, or has an unknown cause, should be reported. You want the raw data without the biases of doctors guessing if something is related or not. Then the data scientists and researchers can clean the data.
Indeed. The extreme version would be to collect data about "all problems, period", and compare the rates of "people who got the vaccine in the last N weeks" against a control group. Like looking at "excess deaths" to estimate the deaths caused by COVID. Picking the right control group might be tricky, though...
Yeah, I looked at doing some analysis for a vaccine related injury. There aren't really any control groups for the mandatory vaccines. The best you can do is try to time box it like you're talking about. Even using groups that may not vaccinate (certain religious sects usually) may have issues with the sampling not being random due to genetics and demographics in those communities.
I wanted to do the time boxing like you suggest, but access to anonymous records with that level of detail and with a sufficient size is not easy to come by (as a lay person for free at least).
