The film was based on Jim Lovell’s book “Lost Moon”. Lovell says the ionization blackout generally lasted "about four minutes". Mission control would begin to hail the Odyssey at four minutes from signal loss. The mission control team which was on duty at the time had been working, according to Lead flight director Gene Kranz in “Failure Is Not An Option”, almost continuously for 80 hours.

“the blackout is the toughest time in a mission for the teams. Every member does his soul searching, reviewing the decisions and the data, knowing we had to be damn near perfect and knowing how tough perfection is. Every member of our team on the ground, whether at the consoles, in the back rooms, or seated with SimSup, shared this common agony.”

Their main concern during the blackout was whether the Odyssey’s heat shield was in good enough shape to protect the crew from 5000 degrees of re-entry heat.

Here’s Lovell regarding blackout time:

When the fourth minute ticked away, a number of men in the control room craned their necks, casting glances toward Kranz.

“Alright, Capcom” the flight director said, grinding out the cigarette he had lit four minutes ago. “Advise the crew we’re standing by.”

“Odyssey, Houston standing by, over.” [Capcom and astronaut, Joe] Kerwin called.

Nothing but static came back from the spacecraft. Fifteen seconds elapsed.

Try again,” Kranz instructed.

“Odyssey, Houston standing by, over.” Thirty more seconds.

And Kranz again:

“We were now almost a minute past the expected signal acquisition time. Still no response. Seconds turned into minutes and minutes into infinity. A sinking feeling, almost a dread, filled the room. When the wall clock rolled past one minute, we wondered what the hell had gone wrong. I wanted to smash something, hold on to something. Was there some screwup in the communications setup or relay? I told myself: they are there; we just are not hearing them...

We were 1:28 past the expected acquisition time when a crackly report from a downrange aircraft broke the tension: “ARIA 4 has acquisition.” I pounded the edge of the console; the room erupted… Kerwin called again and a few seconds later we heard, “Okay, Joe!” Just two words, but the intensity of the relief was overwhelming.”

Returning the Aquarius LEM to Earth, something never intended to happen, posed it’s own problems. Much of it would burn up on reentry, but the LEM was meant to be powered on the moon leave behind scientific instruments powered by a small nuclear fuel rod encased in ceramic designed to withstand the heat of reentry. This was a precaution in case the ship exploded in the atmosphere after launch, expelling the nuclear fuel who knew where. Despite the rod's indestructible packaging there was concern about where exactly to drop the LEM. The flight dynamics team chose a spot of extremely deep ocean near New Zealand for the lifeboat’s final resting place.

EDIT: fixed after a correction by u/standish_