What kind of toilet tank is this?
I suspect the water level is set too high, so it's not emptying fully. I'd try adjusting the fluidmaster fill valve (the black thing on the left) 

Here is a link to a troubleshooting guide for that toilet, check the poor or sluggish flush sections.

http://www.watermatrix.com/proficiency/pdf/resources/Proficiency-Troubleshooting-Guide.pdf

Those fluidmaster fill valves are cheap and it may have been replaced once already and not been adjusted the same as the original. 

It may also have been that the toilet sat unused for a while allowing the algae to grow and just killing it off once by scrubbing the toilet clean will prevent it from growing back with normal toilet usage. 

Using bleach and tablets in the tank is generally not a great idea because the chlorine breaks down the pvc used in the plastic parts. I know the fluidmaster parts always have a warning against it and the guide for your toilet also mentions not to use them.