How can you say this with a straight face when day in and day out Google and Amazon are top stories on Hacker News? Azure is the second largest cloud platform, it's pretty relevant.
The one area we've consistently had real issues is with static IP persistence and VM location. At times, between our portal and an RDP session I've seen up to 3 different IP's for the same VM. Our VM's invariably lose their static IP's during reboots, which is a real nightmare because some of our vendors require IP white listing. We also can't seem to confirm that our servers are geographically where they're supposed to be. If we try to geolocate a server in US-West, we variously see it in other parts of the country, or even the world.
I think you can do this from the Azure CP now, I am not 100% sure.
Your IP should not flush on reboot though, that should theoretically only occur if you're doing cold boots/shutdowns; but that's a no-no in any cloud environment unless you have a reserved IP; which is why you are encouraged to use cnames instead for domain management, etc.
As far as the region problem, this can happen if you're using something like a scale set or load balancers. That could throw off a trace route. Also making sure your storage account, etc are all in the same region is fairly important.