Should I be looking closely at vendor items at higher difficulties?
I've found that they can be useful, especially when you first transition to a higher difficulty.
If you are buying items you will probalby find cheaper and better from the AH. I prefer to get upgrades from killing where possible as it give you some reason to explore the dungeons that arn't part of the main quest line.
Absolutely look at the AH first, where you can easily sort by buyout and pick item traits you want. Often you'll be able to find something much faster, fits your build exactly, and cheaper than checking out vendors.
Having said that, magic find items are horribly over priced right now so I always check out the vendors (at least on inferno) to try and find upgrades for that, especially MF amulets and rings.
Yes, you absolutely should - not just for yourself on the occasion a weapon with decent DPS might appear, but also for the times when vendors stock magic rings or gloves with high primary stats and boosted Attack Speed. Not only are these great for personal use, but they're also often sellable on the auction house for more than their vendor cost.