One main issue would be having the mobile phone in roaming. Without roaming, your phone mught not get a network overseas. Although most, if not all, network providers now allow auto-roaming. You can just probably ask your network provider to switch the roaming mode on to be sure.
Another issue would be the roaming charges, especially the data charges. I don't use my data/internet when overseas. It will incur a huge bill if I use that. So I always would connect to wifi, as much as possible. One way of solving this problem though is you can probably just buy a local prepaid sim card in that country, especially if your phone is unlocked.
