Dropped a player, and another team was able to pick him up a few hours later, thought it took till after all the weeks games ended?

Most waived players have a locked out time. When the league is set up the settings are posted.

Rule #1 in Fantasy sports, KNOW YOUR LEAGUE RULES.

One time I picked Anthony Thomas and started him and he had like 170 yds an a Touchdown!!!!

If you were able to drop him, that means he hadn't played yet. Therefore hes not locked and if he's a FA that hasn't played, he can immediately be picked up. 

The commissioner of your league can add a player at any time.  It's one of the perks of being the commissioner.

If it was a player you picked up during the week and then dropped later, that player goes to free agency rather than waivers. It's been this way for several years now because some owners used to pick up and drop many players in a week to prevent other teams from being able to get them.

That happened to me too..

It never usually happens that way.

It was truly a head scratcher for me.

I wrote it off as a glitchy fluke.

I guess you don't know your league's rules.  I certainly can't see them from here.