Diving with a Inspiration Close Circuit Buddy
There are several articles available on the web advising how to change your diving practices when your buddy suddenly sprouts an Inspiration Rebreather but most of them are far too sensible to deal with the scare stories about.

Nobody ever accused me of sensible so bring on the fables.....

The task loading is such that on the descent they are totally brain locked.
They do have to look at a gauge every minute or so and click one switch somewhere on the way down. Oh, and yes, they do have to inject diluent into the counterlung but the hand that does the dry suit inject and the nose pinch has long since learned to do that by the time they got to the end of their training so they probably don't notice they're doing it and if they forget they find the breathing goes a bit tight as a hint.

They will be killed by oxygen spikes on a fast descent.
Fiction. The fable goes like this:
They are on the surface breathing 0.7 bar O2 so that is 70% oxygen in the loop.
A crash descent to 40 meters and that 70% is 3.5 bar of Oxygen.
How dead can you get?
But the loop contains about 5 litres of gas and at 40m the original 70% is now 1L of gas so if they haven't added any diluent they must have flooded the loop. They will be drowned long before they ox-tox. Add the diluent and they are getting a gas they can breathe on the bottom so the extra 4 litres of the mix is now air. I make that 30%, 1.5bar O2, a bit high I grant but we did have to tie the shot weight to their crotch strap and throw them over the side to get them there like that.

They are stuck at one depth once they are down.
No that's just showing off. Once you trim for a depth you stay there regardless of how you breathe. To go up and down you swim or you have to use the wing or fiddle with the quantity of gas in the loop and it ruins the *I only used 30 bar on that dive* joke afterwards if you do too much up and down.

They will go hypoxic and die on the ascent.
Well if all the equipment is functioning even they are diving heliox at 70 meters the loop may only have 16% oxygen in it so that might be a bit nasty on the surface but even if you shut off the oxygen tank so it can't fix things and then turn off the computers to stop the desperate beeping driving you mad it's still breathable.

If they miss a computer check they're meat.
Nope. It's just a check. The manual says that if you don't check the instruments you will die but it takes a failure to make it happen. Failing to check the computer is safer than failing to check the SPG and running out of air on O/C because, given time, I promise you that you will run out of air but I can't promise an equipment failure. The problem is keeping the checking habit up in the face of brain stoppingly dull correct readings which is why the check-check-check is plugged so hard on rebreather training.

They should be a dive god before they attempt CCR diving.
Just more to unlearn. The humble novice will take orders like doing only simple shallow dives for the first 20 hours much better than *I've done 500 dives* macho man. Unlearning is the problem. The assumption that if there is breathe coming you're OK has gone. You need to know what you are breathing minute by minute.

They take forever to get ready.
Hey this is getting personal! The set up check includes a 3 minute breathing test so you know the loop and oxygen injection stuff is working. It's hard to make polite conversation with the mouth-piece in. Most of the pre-dive checks are done already but the thing is so darn efficient it takes several minutes for a problem to show. I have shut off the oxygen tank valve in the pool with 0.7bar of oxygen in the loop and just mooched around for 11 minutes before the low oxygen alarm sounded at 0.4bar.

They don't carry enough bail out gas to handle a problem.
Well two points. Bail out to open circuit is the last thing you do when every other avenue has failed. Once you have accepted that then the rule is better bent than dead and the fact that the mix the rebreather gives is virtually optimum at all points on the dive means that most dives are safely close to no-stop anyway. You can put yourself on the surface with 30 bar in the 3L diluent tank so full isn't really an issue. The oxygen tank is almost never full as you just can't get oxygen at 230bar pressure most places unless you're a smug brat with a Haskel booster. <<smirk>>

They are a novice again.
They are a novice rebreather diver. They haven't had a lobotomy to hack out all that rescue/leadership/nitrox training and experience. They are trying to convert new skills into new habits so things just happen. The new rule is that everything is only promised for two minutes. Check the computer and you have another two minutes. They did this in training - turn off the gas and swim up and down watching the displays and see how long it takes to go pear shaped. When all you worried about was the SPG you could give it longer. Rebreather diving is not hard, it is not complex, it does not involve any arcane knowledge. It just involves new habits and new habits come hard.

OK so what do I do?
You need to know four rescue items. Everything you learned about surfacing the casualty and giving oxygen still applies. The rebreather is just another way of delivering breathable gas when under water. There is no way giving oxygen to a diver at the surface can make matters worse even if you think they were hyperoxic at depth.

So what are the real problems?
  1. Hypoxia. Low oxygen.
    The danger is that something stops the computers, the oxygen inject and the alarms. The loop oxygen level drops. They aren't doing their computer checks so they don't notice but the loop will last quite a long time. Finally they come to ascend and they still don't notice. They are breathing, say, 0.5 bar of oxygen at 30 meters. The alarm would have gone at 0.4 bar and woken them up to the problem but at 0.5 bar they only have 12% oxygen in the loop. Only the depth is keeping them alive. If they start to ascend they will be dumping gas from the suit, the wing and the counterlung but as the absolute pressure drops so will the partial pressure in their body. They will just fade painlessly away.
    A rebreather diver must watch the ppO2 especially before an ascent. They can manually inject Oxygen and wait a few minutes and then ascend keeping the loop rich. They have a problem as they now have a huge loading of Nitrogen so they need a plan to do forever in deco stops but the rebreather can deliver just that. They can do leisurely stops up to 5 meters or so then flush the loop with 100% oxygen and wait out their scrubber time. An hour long stop will probably take less than 20 bar of oxygen.
    The best thing you can do for your buddy is to watch for the handset check. Just tick it off in your mind. If they are checking they are OK.

  2. Hypercapnia. High Carbon Dioxide.
    If the rebreather is working correctly the diver is breating a gas almost devoid of CO2. This works well and everything is happy. However if this is not so, either because the scrubber material has become exhausted or because some fault allows the loop to bypass the scrubber, breathing CO2 at depth is very bad.
    On the surface elevated levels of CO2 cause the body to react much as if the CO2 were being generated internally and you breath faster to exhale the offending gas. This is a built in, not negotiable response. On a defective rebreather however this will not solve the problem and the diver is caught in a spiral of 'must breath more and more'. The only way to break the cycle is to stop breathing CO2 so get off the rebreather loop. Since pausing for breath rapidly becomes impossible divers need to have a plan to escape from the trap before unconciousness gets them. Mine is a switchable mouthpiece where I can go to breathing my diluent feed but I have switched to injecting the gas I inhale and then exhaling through my nose so the gas does not move round the loop.
    It is estimated by some that CO2 has killed more divers than all high and low oxygen problems put together.
    How would I help as a buddy? I'm not sure. I've been caught in that trap and I had to work hard to escape. I think I'd start by stuffing a reg in their face to try and help them to come off the loop, then I'd DIL flush them and keep DIL flushing them but failing that I'd lift them. Better two on a helicopter than one in a box.

The other real problem is that once you know what's going on you want one too.
Been there myself.