Those who understand Japanese better than I do, please correct me, but I don't think it makes sense to try to understand "koto mo aru" as one expression. "koto" is used to turn the preceeding phrase into an object (nominalization), and "mo aru" means "also exists", in the sense of "also happens". Watashi ha Osaka ni iku koto mo aru. = As for me, the thing/event of going to Osaka also exists = I go too Osaka, too. Similarly for "the event of not going to Osaka" or "the event of having gone to Osaka". "Sometimes" isn't mentioned explicitely anywhere, I would have expected "tokidoki" etc. somewhere in that case.

Watashi wa Osaka ni iku koto mo aru. = I go to Osaka, too. Watashi wa Osaka ni ikanai koto mo aru. = I don't go to Osaka, either. Watashi wa Osaka ni itta koto mo aru. = I've been to Osaka, too. koto mo aru = I have that experience, too. Compare with "koto ga aru".

mo(も)　aru(ある)　It means "have (done) sth. too" わたし　は　おさか　に　行くこと　も　ある。I go to Osaka,too. わたし　は　おさか　に　行かないこと　も　ある。I don't go to Osaka, too. わたし　は　おさか　に　いったこと　も　ある。I went to Osaka,too.