Yes, complete pause of display as though it was not receiving any more input. Autoscrolling off doesn't help when I'm trying to look at the end of the data.
There are times that a program will output a long string of data every 100ms or possibly even faster. Reasons for this are varied but useful in program debug or data/sensor analysis. To solve the problem, I typically put a Pause function in the program and/or slow the output data rate. But having a button on the Serial Monitor to pause would be helpful.