Ideas
I tested this on a portal server against bots. I could shoot and shoot the bots and maybe every fifth shot were counted as a hit. In the browser menu it shows 32 ping for the servers so it shouldn't be that bad... But when I play against people, the bad connection sign pop ups every now and then. And when I look at the connection charts what the game provides, it shows huge spikes now and then. So I would assume that packet loss is happening from time to time.
Hit registration certainly varies a lot. Some matches are great! I can really feel the difference when my shots actually hit. And on the other end is that can shoot multiple times on a stationary target not hitting it once.
I tested my internet speed/latency with testmy.net
From Finland to Frankfurt Germany 46 ms
From Finland to Tokyo Japan 269 ms
To Google 20 ms