I think most games are plagued by what i call starting in the whom. The game's level system starts at level 1, but many games don't meet very often and thus, many games will go for months in the heroic tier. While this may be all good for some players, others might want to get started a bit higher.
There are a lot of things that have to be considered when dealing with games starting at higher levels; the mechanical stuff, the item management and everything else may be somewhat difficult for some DM's to manage, but a lot of the behind the scenes, the character plots and the character backstories are a point where characters which start at higher levels can really use to their advantage.
How does everyone know each other?
If you're starting at higher levels, chances are, the characters may have already been adventuring together. This means, that the characters can start with a united backstory which develops all kinds of fun ways to grow from there on. Perhaps the characters built up an adventuring party at the early levels and then adventured together from there on. Maybe the characters were on and off allies which united up again for a big fight on the road ahead. There are many ways to go with it.
What have you done?
With characters that start at levels higher than heroic, opportunities for backstories fighting against creatures or enemies which actually had some decent power and ability to stick around is now an option. This allows for future plotlines featuring bad guys from the past which are already pre-imagined in the character's minds.
Lots of other options and questions stand to be asked. Anybody have any other ideas for starting games at higher levels?