Could there be a problem with another tenant storing 15+ large plastic bags of empty water

[RockRaven]

6. May attract rats/rodents as a shelter. They shit and piss indiscriminately in such places.

And, of course, once they have found a nice refuge those rodents chew everything and try to eat everything.

As noted by others a fire hazard both as something which burns readily and something which will get in the way of firefighters if something else is burning and they need access.

And it will trap moisture against the side of the building. Depending on the climate and construction materials/techniques, this could facilitate mold/mildew/fungi/moss or termites/other insects damaging the building.

The landlord should care but you would know best of they actually will or not. Also you're in the best position to judge whether or not it is worth it to try to get them involved -- depends on the various personalities, etc.