On algal toxins, it's worth mentioning that not all species of cyanobacteria form surface-scum; some suspend deeper down in stratified lakes. Normally this wouldn't be a huge problem for bushwalkers, but under some situations (say, a very windy day) that stratification may be disturbed, redistributing the bacterial cells. Just saying, don't judge solely based on the appearance of the surface water (which is usually a reasonable indicator of some aspects of water quality).
Algal toxins are predominantly intracellular. This means the toxins reside within the bacterial cell. This is important, because if you suspect cyanobacterial contamination of your water supply, adding disinfecting tablets to it is probably not a good idea. Oxidisers like chlorine dioxide will destroy the cellular structure, releasing the toxins into the water. Of course, if tablets are your only method of purification, then by not using them you're exposing yourself to other risks like E. coli.
Filtration of the toxins is pretty ineffective - however filtration of the cyanobacteria cells themselves is somewhat more effective. Gentle, slow filtration (e.g. gravity filtration) may serve to remove them in reasonable quantities if you're desperate (gentle and slow so as to not damage the cells).
Oone of the best ways to tell if there's serious algal contamination of the water (in the field) is probably to scoop some up in a pot or cup, agitate it, and smell it. If it smells particularly "earthy", that can indicate the presence of geosmin or methylisoborneol, both of which are indicators of the presence of cyanobacteria. They also, rather helpfully, have a very low odour threshold - so just about anyone can detect them.
Similarly, if after treatment the water tastes "earthy", then steer clear.
Oh, and boiling is, unfortunately, completely ineffective. :\
EDIT:
https://www.nhmrc.gov.au/_files_nhmrc/p ... 131216.pdfThe Australian Drinking Water Guidelines are a great source of information.