I would add at least a couple more.
There are false problems that ask "why doesn't the universe act like I think (for no good reason) that it should?" This includes the hierarchy problem, the strong CP problem, the baryon asymmetry of the universe, and all research invoking the concept of "naturalness."
And, there are contradictory data problems, where one asks why multiple measurements of the same thing (in your current theory) are producing irreconcilable results. These have included the proton radius puzzle, the data based calculation of muon g-2, the measurement of the mean lifetime of unbound neutrons, the reanalysis of CDF data to determine the W boson mass that produced an anomalous result, and the Hubble tension. Usually, in these cases, the answer is that somebody screwed up in one or both of the experiments (at a minimum by overstating the uncertainty in the result), or the theoretical analysis involved, but sometimes, the theory that said the measurements should be the same was wrong.
