My Galaxy S4 will dial a contact (that isn't one of my favorites) when I haven't tried to place a call.
Details about the problem...
This started within a few days of lollipop update.
Usually happens when I open or close the "phone" menu.
Glitch is not there all the time
May repeat the call several times in a row, repeating the call with each attempt to make it stop.
Never happens in my pocket
Always holding phone or touching screen
May not happen for a few days, may happen several times in one day
Almost always happens with one particular contact, but several times it has been other contacts.
It is not calling the last # dialed (except when it is one of those times it does it several times in a row)
Things probably not causing the issue...
I don't have any speed dial numbers stored
"Direct Call" is off, but that shouldn't matter as contact is not displayed on screen before the call is placed.