HRM spikes - question for HRM users

I've faithfully worn my HRM for the last year for running and biking and have seen big gains from generally training in the 'right' zones, but have a question for all you other HRM users.

I can't get a picture of my HRM graph here on BT, but it shows a series of spikes - up, down, up, down... through the whole run.  I can see trends when it gets higher when I run faster, but I tried to use the alarm function over the weekend to keep my HR in zones 1-2.  It drove me nuts!  It was beeping every few seconds, but then as I watched (and kept running at the same RPE) it would go back to Z1 - so it was roving around Z's 1-3 with the occasional foray into Z's 4-5!  All while I was running a very steady slow easy Z1-2 RPE.  Average HR ended up being mid-Z2 for the entire run, which felt right, but I can't imagine doing workouts where I keep it in a certain zone for a certain amount of time or distance.

So, what's wrong with me or my HRM?  Or is this normal?  Do your HR graphs look like a child's scribbling?  ANd finally, how can I do specific HR workouts if I can't trust the readouts at any one time? 

Thanks!