License borrowing was a hotly anticipated (and largely successful) feature of ArcGIS 10.0. That said, there are a number of issues that do affect many organizations with borrowing.
ARC/INFO Licenses (Only) Cannot be Borrowed
With the initial release of ArcGIS 10.0 came a problem with the ARC/INFO type license that prevented borrowing for this license only.
A patch was later released to fix this:
The patch must be applied to ALL client systems that need to borrow the problematic ARC/INFO license. For some organizations this is a daunting/impossible task.
A much more palatable fix (from the customer's perspective) is to have Esri Customer Service obsolete all ARC/INFO licenses, and create a new set of ArcInfo (notice the lower-case name) licenses for the customer. This is much more palatable because this requires only a single change action: Authorize the new set ArcInfo EFL licenses on the license manager.