This theory has a couple of corollaries. First of all, if you're aware of it, realizing that this psychological effect happens can allow you to specifically suppress it. Second of all, there is a sort of natural alternation between good/serious relationships and bad/nonserious relationships, because the problems in good relationships tend to be minor, which gives you unimportant criteria in your next relationship search, while the problems in bad relationships tend to be fundamental, which gives you important criteria in your next relationship search. In other words, if you have a great relationship where the problem is that the person's bad driving drives you up the wall -- maybe it ends because of circumstance, or because they break up with you for whatever reason -- then in your next relationship you will look for a good driver. Obviously this is no one's actual primary happiness determiner, so you will end up with a good driver who is not particularly well suited for you in other ways.
Another corollary is that the best relationships should, by the theory, tend to follow substantial periods of being single. These periods of being single have a damping effect; you no longer have the visceral experience of missing something in particular in a relationship, and it allows your desiderata to regress towards the mean of your actual values and the actual attributes that make you happy. Of course, no one's relationship-picking process is that quantitative; I'm just translating what's going on underneath into scientific terminology.
The contrast theory of relationships is very clear in my life. Basically all of my relationships follow this pattern. The attributes in question (which were missing from a previous relationship and which the next relationship was selected based on -- again all of this was unconscious) are, in no particular order: adventurousness, beauty, coolness, depth, emotional stability, excitedness, hotness, idealism, kindness, lightheartedness, quantitativeness, stereotyping, verbal, weirdness, and wildness. (Okay, I admit that they are clearly in a particular order.)
Some of these have of course gone better than others. In writing that list, it actually seems to me that the best relationships don't really match up with the things that I would think are most important to me, so maybe that particular corollary is not so true.
The theory is in some sense unintuitive. You would think that life would be a series of relationships which gradually converge on what you want; i.e. each relationship should be someone better for you than the last, as you increasingly discover what matters to you and what doesn't. In other words, each relationship death should show you something that matters, and that thing should simply be added to all the other things in the past that you know matter to you in relationships. But in practice the contrast theory states that instead of augmenting those things, it overrides them. It's not particularly productive, but I think that's just the way it is.