Dan Szymborski of ESPN's Baseball Think Factory breaks down the remaining needs of every team in the majors in this post. Here's what he says about the Angels, who he ranks 30th out of 30 in terms of pressing needs:
They got their holiday shopping done early, giving out $334.5 million to free agents this winter. That's more than the next three biggest spenders (Miami, Philadelphia, L.A. Dodgers) combined at $326 million. The AL West should be a whole lot more fun, but the Angels will probably have a quiet January and February.
Outside of stealing a third baseman like Taylor Green from the Brewers, the Angels will give Mark Trumbo every opportunity to try to handle the hot corner.
I agree that the Angels don't have much more business left to conduct, but I still think they'd like to add an experienced closer and give Jordan Walden the opportunity of learning while he pitches the eighth inning for a while. Also, I'm less optimistic about Trumbo being able to play third base regularly based on conversations with him in the past. Plus, they have spare parts they'll likely trade away, including Bobby Abreu and one of the utility infielders (Maicer Izturis or Alberto Callaspo), though it might make more sense to wait until spring training, when other teams' needs tend to become more acute because of injuries.