No, nobody sensible cares. But the stuff people are suspicious of is supposed to be regulated so that your executions are only improved. If somehow this isn't true, it should be a bright line crossed and a big scandal with people going to jail or at least big fines.

Then again, if you panic over a "flash crash", then I guess you should be concerned about liquidity?

I think you may care actually. To give an example, I was holding a stock for several years that recently went up in price quickly, without much change in the underlying business. Simply, analysts started changing their rating on it. When this stock got high enough, I started to feel nervous, and I was watching the market open on a day when I was prepared to sell. Immediately, the stock started to tank, and I sold it right away.

I sold it at a good price, and even though I was a long term investor, I made a short term decision to sell based off the (IMO) extremely irrational price.