The reason for this error is that between .NET 2.0 (including Silverlight) and 4.0 the [Extension] attribute moved from System.Core.dll to mscorlib.dll.
Xamarin.iOS 6.2 (and earlier) were based on a superset of Silverlight (aka the 2.1 profile). So the [Extension] attribute was located in System.Core.dll.
Since Xamarin.iOS 6.3+ the product was re-based on Mono 3.0 and the profile was updated to use the newer 4.0/4.5 profile. Now the [Extension] attribute is located in mscorlib.dll.
In your case you had a binary assembly compiled against the newer (4.0) profile. That assembly had a reference to mscorlib, Version=4.0.0.0, ... to find [Extension] and would lead to errors if built against the older Xamarin.iOS (6.2 and earlier).
As you found out the easy solution was to update to the latest Xamarin.iOS release. Another way to solve this (without updating Xamarin.iOS) would have been to rebuild (if you have the source) the binary assemblies of your project against the assemblies (BCL) shipped with Xamarin.iOS 6.2.