Hotels should definitely increase the security personnel on hand to ensure that their residents are safe. This is especially true for those that have convention centers, where large quantities of people could be present. It would be most effective to have security personnel trained heavily on the probability of mass shootings and how to deal with the situation should it ever arise.
I am 100% positive that hotels should increase security in the wake of mass shootings, especially overseas. Tourists are the target of a lot of terrorist attacks because they are usually vulnerable and unaware. The places where they are likely to be should always be vigilantly watched and extremely secure.
Increased security at hotels would be a pain, but I think it is necessary to save lives. It is sad that we live in a world where we need increased security everywhere, but that's the reality right now. I think it would help to at least have metal detectors at the doors.
I don' think increased security at hotels is really necessary. Photo identification should be adequate for guests. Too much security is a hassle for the average traveler. Very expensive hotels may need to increase security though if they have famous guests. Those type of guests may be targeted because of their fame.