All adverse events that are reported to healthcare professionals. Patients themselves can also report adverse events. If you go to your GP and complain of a bad headache after a jab, they'll report it. Anything you ingest or take can harm or kill you. For any drug, vaccine, biological etc there will always be a tiny minority who are uniquely allergic to it. There are unfortunate people out there who blister in response to water (!)
The fast acting regression is likely a red herring. Let's take Rett syndrome (something I know a fair bit about) as an example. Child appears to be normal until about 18 months. Getting speech, eye contact is good, engaging etc. then, often very sudden regression. Loss of speech, eye contact etc. they develop autistic behaviours, gut issues, fits. But Rett syndrome is not caused by vaccination, it's caused by a single gene mutation. Unfortunately, the regression often happens about the time of many childhood jabs and so parents, quite understandably, link the two erroneously. When you look much closer at Rett kids though, you see there are very subtle signs predating the obvious onset. The same seems to be true of the bulk of autism cases.
There seems to be a developmental stage where various processes connected to autism and certain neurodevelopmental syndromes kick in/become apparent. Unfortunately that coincides with the age we get a lot of our jabs at. It's pretty simple epidemiology to show that the two are not linked in a causative manner. It's very difficult indeed to explain why we know this to be true to a parent who has seen their normal seeming little girl develop this heartbreakingly awful syndrome.
Autism is very complicated. Most causes aren't as cut and dried as Rett syndrome. We are sure there's no single environmental trigger. We are sure it's a multi gene effect type of thing, but untangling that is mind bogglingly complex. Much, much more research is needed.
People want the answers to be simple. Smoking gives you cancer, uv light gives you melanoma, so why can't autism be linked to one thing we can campaign against? It's just not that simple. The diseases that have a single gene cause, or a simple environmental cause, are in the minority. For most, the cause is complex.