What do you like best?
The UI is definitely the most pleasant and well-organized of any MySQL client I've used. Every schema object is easily accessible and important supplemental information, such as table size and index cardinality is displayed alongside the usual structural details. Sequel Pro is also smart enough to refresh the schema when you change it, either through the UI or with DDL.
The data table view allows entering NULL into a field. Some other clients I've tried either don't support NULL or require annoying contortions to set a field to NULL.
Disconnections are handled mostly gracefully and mostly transparently. "Mostly" is far and away the best handling I've ever encountered, and very nice when connected to a DB over an unreliable VPN link. Sequel Pro can also set up connections over an SSH tunnel, for shops with that setup, and this has worked quite well for me in the past.
What do you dislike?
The table and column completion in the SQL editor is clunky and introduces mistakes more often than it helped me. I ended up disabling it. The SQL editor also has difficulty with complicated DDL syntax, such as stored procedures.
The data table supports only one filter condition. Supporting complex WHERE clauses with a simple UI just isn't possible, so I understand the limitation, but I like the data table and would be fine with a little more UI complexity in exchange for more power.
Recommendations to others considering the product
The price is right and there's nothing better for poking around a database to look at what's there. Use something else to run DDL scripts, though.
What business problems are you solving with the product? What benefits have you realized?
The schema browser showed me tables and indexes taking up much more space than I expected, which prompted some schema changes preventing a costly expansion of storage.