How do I tell whether if it is my oscilloscope or circuit catching mains 50 Hz?
Connect whatever probe you're using to your scope.
Take the ground clip on the probe, and connect it directly to the probe tip.
Now look at the scope. It's now displaying whatever RFI/EMI the it's picking up between the probe tip and the display. Set the scope for roughly the vertical sensitivity you're using to measure your circuit. Or to make the test more stringent, turn the vertical sensitivity up a couple notches.
Chances are pretty good that even with the sensitivity turned up as high as possible, you won't see significant noise.
If you do see some noise, test with a different probe--a problem with the probe's shielding strikes me as a lot more likely than a problem with the scope itself.
But I doubt that'll happen. I have probes that have been used (and probably at least mildly abused at times) since decades before that 'scope came on the market, and most of them still work just fine (the one exception I can recall was pretty obvious too--it pretty much got ripped in half, so the damage was immediately obvious).