The things that you have already mentioned are two of the things that are most often cited as bad things that Jackson did while president (though it is not clear that opposing the Bank necessarily makes him a bad president).
There are at least two other things that you could point to to say that Jackson was a bad president. First of all, he tended to take a lot of power for himself. This can be seen in his ignoring the Supreme Court on the issue of Indian Removal. It can also be seen in how he vetoed more bills than all the previous presidents combined had vetoed. (Again, there is nothing that makes this necessarily a bad thing. Presidents today veto bills too -- it just had not previously been done and so Jackson got criticized for it.)
Another thing that you could mention would be Jackson's use of patronage. Jackson thought that the victors should get the spoils and that pretty much anyone could do a government job. So he gave out government jobs to people who had supported him. Some of these people ended up being corrupt. This also led to Jackson having more personal power because the people in office owed him for putting them there.
Some people think these things add up to him being a bad president. That is a matter of opinion, though.