Get rid of the AC 50Hz noise from circuit
Yesterday I was experimenting with Rigol ds1052e myself and yes you WILL see 50Hz noise with probe without even touching anything. Try to connect ground alligator to the tip of the probe and you will pick up even more noise. This goes away when you unplug probe from BNC. So yes, this is from the probe itself, not necessarily from your circuit. I've seen people suggesting to use coiled piece of wire around ground barrel on the probe, rather than attaching ground alligator. See this link for details http://e2e.ti.com/support/power_management/simple_switcher/w/simple_switcher_wiki/2243.understanding-measuring-and-reducing-output-voltage-ripple.aspx

Also check if your scope has bandpass filter. It might help.