This varies a lot by vaccine. The typhoid-fever vaccine I took in 2003 has "trivial side effects" in the 90-in-100 range, I think --- namely, you feel sick for a few days.
You're absolutely right, I should have been more specific by saying that in the case of the MMR vaccine, trivial side effects are in that lower range, but --as you've pointed out-- that isn't true in all vaccines.
Trivial side effects (small temporary rash) are probably in the 1-in-100 range. Moderate non-life-threatening are probably in the 1-in-3000 range.
Dangerous or life-threatening side effects are in the one in a million+ range.