I've never had issues with my RO/DI trash can (read: relatively open to contamination through unsealed lid) growing anything, but it is continuously stirred with a powerhead and each "batch" of water rarely sits in it for more than about 4-5 days max (I probably top off close to 40 gallons a week).
That said, my saltwater trash can "grows" a brown film on the sides of the container and, if I leave it go long enough without cleaning out the container, the top will start to get a skim even with constant stirring.
Now, the reason I put "grows" in quotation marks is because I'm not certain this is actually growth. The bottom of the bucket gets significantly more nasty than the sides and the accumulation actually hardens to a crust if I leave it long enough. Because it accumulates more on the bottom, only happens in my saltwater bucket, and because it actually gets really hard, I'm more inclined to believe that it is a precipitate of some sort (as opposed to bacterial contamination). However, that probably doesn't adequately explain the formation of the film on top...
I often wondered how much organics are actually present in the salt we buy and whether bacterial contamination (which is essentially inevitable) could be consuming or converting a constituent of the salt (organic or inorganic) that is then able to precipitate out of solution. As time goes between cleanings, the bucket will then harbor these bacteria, precipitate more out of the next batch of water, and then create more scunge. This is all just wild speculation, but something has to be going on here.
If it is a precipitate, I wonder how that affects your saltwater composition over time.