Ian, would you settle for having a palette to paste in the units in a Mathematica expression? Or being able to quickly generate a custom palette that has the units for a particular problem type?
I have an application called UnitsHelper. It's a package, with an advanced and basic palette and a custom style sheet that displays the units in black instead of grey. (It just seems to me that it's important information and should be displayed as all important information. But you don't have to use the style sheet or could change it to your preference.) There are also quick links to Wolfram and NIST documentation. The advanced palette displays all units by group and then either alphabetically or by size. Physical constants are also on the palette. There is a facility for using reduced units such as geometric or atomic units and also a facility to deunitize an expression to use implied input and output units. Also facilities for general decibel units.
If you're interested send me an email from my profile page and I'll send you a Dropbox link.