I had a number of issues with XCode 8.1 which broke all my Xamarin iOS apps. The two older ones, where I used Xcode 7.3.1 to build the most recent version, had their storyboard layouts completely broken after compiling with iOS SDK 10.1/XCode 8.1. The most recent one, which I've build using XCode 8.0, was working normally. After upgrading to 8.1, Monotouch.Dialog's EntryElement wasn't raising the text changed event, rendering my editing views completely unusable.
I've managed to get my dev setup working again by installing iOS SDK v10.0 within XCode 8.1 to get EntryElement's "changed" event back, and XCode 7.3.1 with iOS SDK v9.3 to keep the layout of my older storyboards intact.
The autolayout features are broken in XCode 8.0/8.1, and the "fix" that Apple says it applied in 8.1 didn't work for me.
Thankfully these are all working side-by-side with a single Xamarin Studio / Xamarin iOS setup:
Xamarin Studio Community
Version 6.2 (build 1413)
Version: 10.0.1.8 (Xamarin Studio Community)
Build date: 2016-09-23 15:34:54-0400