Another view of the hanger issue "for the archives" - and for the site I'm working on. Along with a tight chain link, the bent hanger has become a very popular diagnosis. It is important for one to consider that as a potential problem with shifting, and I'm glad there is more awareness of it than in the past. But it's important not to grab onto it as quickly as some seem to do. For one thing, it becomes something to just throw in there as part of a shotgun approach to diagnosis, rather than a logical process.
More importantly the bent hanger option may be plain wrong. Just as the person who suggests that a tight link may be the cause of a once per crank rev click (not possible) suggesting that a progressive problem such as the OP's is due to a bent hanger is not necessarily appropriate. To see why one needs to look at the geometry of the rear derailleur. The derailleur moves a set amount according to the cable movement between clamp and the stop on the derailleur. That does not vary. If the hanger is merely bent inward it changes nothing about that movement. The efficiency of the shift will likely be affected though, as the chain is slightly off vertical as it is pushed and pulled. Of course it may no longer shift to the small cog and may overshift past the large. But there is nothing that would differentially change the position of the top pulley under the cogs as one shifts across them.
Try this experiment: Place your hand in front of you edge on and vertical, with your fingers in line with a window or door frame. Rotate your fingers forward and notice that they stay in line with the vertical line of the frame. Now tilt the top of your hand to the right, but keep your hand edge on and repeat the process. You'll see that your fingers remain in line with the frame. Not only this experiment but experience shows that a simple bend inward of a hanger - the most common occurrence - does not necessarily affect cog-to-cog shifting significantly, and particularly differently as one goes across the range.
What can easily cause a problem is when the hanger is twisted. Repeat the above experiment, but instead of tilting the hand rotate it so that it is no longer edge on and you can just see your palm. Now rotate your fingertips forward in the plane that the hand is facing. The tips of your fingers will rapidly depart from the vertical line of the frame. That is what happens to the top derailleur pulley when the dropout or the derailleur cage/body is twisted. The result is that a derailleur that works fine in smaller cogs or on one chainring will not work properly on larger cogs or another chainring, as the pulley rotates to accommodate the difference in chain wrap.
Yes, it's fine to check the alignment if one is able to do so, but it's still important to approach a drive train problem in a thoughtful manner. Buying an alignment gauge is foolish for most individuals who don't own multiple bikes. In the past twenty years I have had to align the hanger on one bike that I've owned, and even in a shop it's not a common need on bikes that have 8 or fewer cogs.