We've all seen people retweet compliments about themselves, often with a simple "Thanks!" at the beginning. Some say it's good publicity, but I'm not a fan. Here's why:
1. In general, retweeted compliments neither inform nor entertain me. From a content perspective, I just don't see the value.
2. Bragging is annoying. Most people don't brag this way in the real world. To put it in context, let's say someone calls you the most brilliant person on the planet. Now imagine walking up to a bunch of acquaintances and saying, "Hey guess what! Somebody said I'm the most brilliant person on the planet." Who does that? (And saying "Wow, thanks!" at the beginning only makes it a humblebrag, still not a good look.)
3. It's preaching to the choir. Your followers already like you—that's why they follow you. You've got their attention, so you're better off telling them something they don't already know, making them laugh, or delighting them.
Testimonials are certainly valuable for companies and entrepreneurs, but I'd argue that Twitter isn't the place for that sort of marketing content. Of course there are exceptions, though. For example, if someone compliments you in a tweet with a link to your work or a review of your book or something else of value, then retweeting is another way for you to share content your followers will care about. That's a different story.
I understand why retweeting straight-up praise is so tempting, and even why some people think it's a good marketing move, but I'd prefer a Twitter without it. Here's my advice: Next time you get a compliment, thank the person directly, pat yourself on the back, and for the love of your followers, don't RT.
