The absolutely worst two things which happened to Blogger during the last few years are, IMO:
1. What I percieve to be excessive use of JS. You can't even load a blog post there (well, at least, couldn't last time I visited a dot-blogspot site) without an on-page spinner and a bunch of stuff apparently happening in the background.
2. The tld-redirect crap. Admitedly, I had actually thought a similar mechanism to be benefitial prior to seeing an actual implementation of it but I mean, come on, does this not annoy others? What's the advantage of that anyway? Google is capable of geographical load balancing with IP addresses alone just fine, what's the deal?
Disclaimer: These are my end-user reactions. I have never operated at the scale Blogger does so there may be reasons I am not aware of.