Common problems: Age makes these higher risk
The screws that hold the toilet down may be so corroded they shear when you try to pull them.
You can crack the toilet base if you over torque the screws.
The drain seat in the floor may be badly corroded and not reusable (older cast iron ones). Removal of the screws make break off part of the drain seat.
If you do have to get new screws they may be the wrong length unthreaed shank too long or entire bolt length too long.
You may have problems getting the water line re-sealed after disconnecting it.
The gasket at the water line entry to the tank may start leaking from being moved around.
The water line shut off valve will most likely leak after turning it on and off (just retorque the top part to solve this.
The toilet may (probably will) rock after you put it back down unless you get the wax just right. (Bead of caulk around base solves this.)
The tank to base seal will probably start leaking after being disturbed. Screws holding tank to base may be too corroded and sealing washer cracking from age.
That pretty much sums up 25 yeare of lanlord problems.
Have fun.
PS Start the job early Saturday morning so you have 12 hours of hardware store access if anything goes wrong.