A Liz Moyer short in this weekend's Wall Street Journal called out the easiest ways to check a registered broker dealer's background. To see what is on file use the BrokerCheck tool on the finra.org website. The Moyer short also notes the advisability of checking with state-level broker regulators since BrokerCheck doesn't capture every investor complaint. A list of state regulators can be found here.
Keep in mind that quick and thorough seldom amount to the same thing so be aware that additional checks might need to be conducted (e.g., lawsuit, lien and judgment searches).