Some tricks you can try (if it really bugs you, though):
give the characters identifying traits, occupations, actions (the blonde, the doctor, smoking cigarette after cigarette) and refer to them when you refer to the character;
give the character more than one name (JRR Tolkien did this with Strider/Aragorn/Isildur's Heir/Elessar, Eowyn/The White Lady of Rohan/Shieldmaiden, Arwen/Evenstar, Elrond/Half-Elven, etc) and let the other character's choice in how they address each other be part of their own characterization (you have to be careful with this, though, because it can really confuse your readers);
give the character individual ways of speaking or moving or their own identifying concerns, and let those show which character is being referred to (doesn't use contractions, or says, "ya know" a lot; runs his hands through his hair or clears his throat continually; keeps bringing the conversation back to her single-minded concern or does things to show that's the only thing she's thinking about.
I hope this helps a little.
If you stick with that rule, the reader gets used to each paragraph being "about" a character assigned as the subject, and thus knows that the pronouns in the subject positions later in that paragraph are still referencing the active character. Use the names of inactive characters rather than pronouns, if none of them are the active character, using their names shouldn't be too burdensome.
Your chosen POV can have a pretty significant effect on this as well, and you don't need to give every character equal time as the active character. You also can start a new paragraph using the same active character without necessarily having to re-establish the pronoun reference. But once you're down to using the characters' names once or twice per paragraph, it's not really useful to cut back any further.
I'm okay with using alternate references, but you should use them selectively to add meaning. For instance, let's say Johan is a police officer, Mary's husband, and Greta's older brother. When Mary is the active character, Johan should probably be "her husband" or "Johan", not "the officer" or "Greta's brother". On the other hand, it might be that she is interacting with his role as a police officer or Greta's brother. Unusual, thus worth indicating.