I had read the reviews that complained about download time for the game so thought I would get around that by buying a physical copy for myself and a friend despite it being free on the PSN store (Also the other copy was a gift and it is hard to wrap a free download). No such luck! we both have pretty solid broadband connections and still and to endure a huge update and download.
His took 17 hours. Mine is currently a work in progress, and doesn't look like it'll be far behind that!
Once this is complete though it is a fun game. There are a lot of the animated series voice actors working on this (Mark Hamill's joker, and Kevin Conroy's batman for example) and a huge game world to complete missions or just mess about in and explore. the powers also translate well from PC to console using the shoulder buttons to quick select your powers, as you normally would with the F or number keys on a keyboard.
That's not to say it's perfect. there are three power sets that are only available with the purchase of DLC, but give no indication of this in the character selection, and I also ran into instances of other players waiting in mission critical areas to ambush and bully other players. Also if you're sticking to the free to play version you'll find your inventory quickly becoming full, forcing you into pretty tight item management.
But these criticisms are a pretty common occurrence with a lot of on-line games, and personally I thought the latter two added to the challenge. So consider yourself pre-warned. but if those don't put you off, and you have the patience for the download give it a try. What do you have to lose when it's free to download and play.