Using a different tense in a dependent clause?

Solution 1:

Normally, when the main clause is past, verbs in any dependent clause are backshifted (to past, unless they were already past, in which case they will usually be shifted to past perfect).

There is an exception, where what is stated in the subordinate clause is timeless, or still continuing:

He said that he was/is living in London now.

If he is still living in London now, then either is or was is possible.

But your example sentence would be very unusual: the only reading that makes any sense is that people have continued to slam the doors right up to the present.