What do you like best?
For clients looking to gain followers that will be a meaningful audience and not robo/auto-followers, this is a good tool to have at their disposal. Their search engines work to target the exact followers they are looking for without cheapening the brand just to increase their presence online.
What do you dislike?
There isn't a good overview of tweets (like Tweetdeck or Hootsuite provide) and there is also no feature to schedule tweets in advance. This is not the right tool if that is what you are looking for.
Recommendations to others considering the product
TweetAdder is a product for clients looking to gain many followers quickly - it is not designed to gain a better understanding of your tweets/mentions/interactions.
What business problems are you solving with the product? What benefits have you realized?
This makes it easier to manage different clients needs and saves time overall.