When Picard gets the ship's doctor to erase Sarjenka's memories, is it ever explained how they can erase specific memories or will there be "collateral damage"?
We can pretty much assume that memory wipes are fairly common in the 24th century, since the same thing was done to Voyager's EMH at one point. Sort of their version of electroshock therapy. Of course the best answer to the question would be something like "What memory wipe?"
Well the Doctor being a computer program can be explained away... sorta, if you don't believe he's sentient. Another disturbing thing in that episode is that Ensign who the EMH let die. Just imagine her funeral... "Though you may be gone Ensign so and so, you will never be dead so long as you remain in our memory.... the funeral is over, Tuvok... purge all computer records of her existence."
Erasing short-term memory is "fairly" "easy", hell a good knock to your head will do that NOW. It's the biological equivalent of erasing and Etch-a-Sketch or clearing out your RAM by rebooting a computer. The more complicated part is to erase long-term memory which is like deleting something off of a DVD or... okay there's no equivalent for the Etch-a-Sketch. Even the "stored" memories of her experiences talking to Data (on biological level) would be "easy" to find since they'd be the most recently created neurons in the part of the brain that stores memories. With a wave of the hand to accept that they've mapped the entire human brain and can scan it at the quantum level it's not too much a stretch to accept they can erase short term and newly created long-term memories.
The memory wipe is a proud Star Trek tradition. It's as renowned as time travel or warp core breaches
If memory wiping is commonplace why did Picard ask the aliens in Clues to use their advanced technology to do it?
Probably because he knew this xenophobic species that wants no evidence of their existence anywhere wouldn't trust outsider to do it.
I wonder why they had the Sarjenka character as a little girl? Maybe they worried that a little boy wouldn't tug the heartstrings as much?