The main problem for a tourist in Jaffna is the fact that - contrary to other places in Sri Lanka - very few local people speaks english. It's due to years of war and isolation of the city. Of course, everybody wants to help you, but there is still a "language barrier". So if neeeded ask the soldiers - most of them speaks at least basic english.
In Jaffna, more then in others parts of Sri Lanka, the army is omnipresent and strongly armed. Checkpoints like this one are almost everywhere, so you need to carry your passport all the time. But the soldiers are quite friendly and helpfull, and big part of them speaks basic english.
But don't take an exemple from me and don't try to make the pictures of them or of the checkpoints. They really don't like that! :)