The thing with mice is, if you can stick a biro through a gap (say, by a door frame) then a mouse can get through it. So, it's all very well catching mice in the flat, but you also need to work out where they're coming in and stop it. Those electronic things can be useful, and if the letting agents have been round and are taking the problem seriously then that's a good start.
Mice will eat all kinds of stuff, and can get into the unlikeliest places. Make sure all your food is stored in airtight containers to put them off (they may eat through a bag or box to get at pasta or cereal, but they won't eat through a jar or a tin). Don't assume that food is safe because it's in cupboards, and don't assume that they won't eat something as it comes just because you wouldn't - they'll eat Oxo cubes, for instance, given the chance. If you reduce the amount available for them to eat, they'll have less reason to come to your flat. They'll eat other stuff, though, so that doesn't solve the problem; you still need to use traps/poison.
I don't think you're under-reacting - it's not the end of the world - but better to take it seriously than find yourself overrun.
On the plus side, if you've got mice you know you don't have rats, as they don't tend to occupy the same spaces!