When you say slime I think of blue green algae or Cyno bacteria. But it could be diatoms as Tex Gal says. If it is brown then it is diatoms, if green (sometimes red) then it is cyno. Here are some sites for ID...
http://www.aquariumalgae.blogspot.com/ or
http://www.floridadriftwood.com/alga...ification.html
Diatoms will go away in time but cyno will need to be treated with E-mycin or a blackout. See this site for instructions...
http://www.aquariaplants.com/alqaeproblems.htm
The plants that dried out will most then likely loose their leaves, so keep a watch out on that. Remove any leaves that start dieing, just cut or pinch off. As long as the root systems where not damaged then the plants will be fine & new leaves will regrow.