"There are some exceptions to these, but I will exclude these for now, since they are a bit technical."
Take for example the Anomalous magnetic dipole moment of the muon [1], it is a measurement that do not agree with theory, but it is far from being the centre of attention for physicists (certainly some people do have that as their main goal to explain, but in general).
So indeed, there are things that do not match up, as well as the need to find a new experiment that gives something new (in the sense: The anomalous magnetic dipole moment of the muon is not enough of a hint to find the "new theory" (it seems).)
[1] https://en.wikipedia.org/wiki/List_of_unsolved_problems_in_p... The 11th point under that section of that article.