It isn't necessary to include the 'should' - it just adds a slight nuance. It adds the flavour of - If you happen to run into difficulties; if it should transpire that you experience difficulties. Perhaps the assumption is that you are unlikely to experience any problems, but just in case that does occur...

As Hilary says, it's all a question of how likely this is to happen. By saying " If you run into difficulties, please tell us as soon as possible. " the speaker is suggesting that it is very likely that the other person will run into difficulties. The use of the modal form 'should run' has the effect of making the possibility more distant, and therefore more improbable. It's a kind of subjunctive, used for more hypothetical situations. " If you should run into difficulties, please tell us as soon as possible. " is equivalent to saying 'I don't expect that you will run into difficulties, but, in the unlikely event that this should happen...'. I hope that helps.

Yes, you don't have to include "should," the sentence works without "should" in it. In this case, it means, "If you [happen to] run into difficulties," which isn't necessary because the sentence has the same meaning either way.