Block problem

Is your server lagging?
If not, do you have any problems with your mouse?

My advice, release your mouse button earlier
It seems like a problem either with your mouse (your button isn't accurate enough, so your pc thinks you are still holding the button and places/breaks the block) or the server has some kind of lagg issues (you can also check that in the console, if it says something like "[WARNING] Can't keep up! Did the system time change, or is the server overloaded?" it is lagging).

I once knew a plugin with a command which let you set the rate of setting/breaking blocks, so how fast you can place/break blocks (for example in creative mode you can place/break blocks much faster than in survival mode). But I really don't know anymore which plugin it was... I think something like Commandbook, or Essentials,.. but I haven't refound it...