Rent controls are just a short-sighted way of giving hand-outs to people who are politically connected or otherwise good at navigating bureaucracy. It's a price ceiling, with all the classic issues of them: shortages, quality reduction, search costs, deadweight loss, and misallocation of resources.
Shortages: More people want apartments than can get them.
Quality reduction: if you're in a rent-controlled apartment, the landlord knows you aren't going anywhere, so why would they improve the building in any way that they can avoid?
Search costs: joining a decade-long waiting list for an apartment. Fun.
Deadweight loss: Developers want to build places that people would benefit from renting, but they don't, because it's illegal to charge rates that would make them money.
Misallocation of resources: someone with a $400/mo rent-controlled apartment in a prime location in downtown SF will keep it forever, even if they only use it a couple weekends a year. Or people commuting from SF to Mountain View can't trade apartments with people commuting from Mountain View to SF, since they're locked into their rent-controlled place.