The ECG signal at TP6 looks fine to me. After a 40Hz lowpass, you'll see a good signal, as DrSchweizer mentioned already. What you've seen on the scope is pretty much what I've seen for all the 2-electrode implementations I've examined. Yours actually seems rather good, DC stability and amplitude consistency is excellent.
I'm curious how they implement that filter. All implementations I've seen use a software filter, because you need a high filter order for good results (block 50Hz hum, but nothing at 30Hz and below in order to get good fidelity on the QRS complex), so its probably cheaper to do it in software. Then again, there are a large number of components on that board, maybe they do have some filtering on the board?