Real plaster is very hard so what you have is probably normal plaster and anyone who does plaster work should be able to fix it. If you want to diy the repairs you should be able to find repair info for plaster firly easily in books or online.

Regarding your thermostat. Does it shut off at the same temp consistently or are you saying it sometimes shuts off and sometimes doesn't. If it's consistent then your best solution would be to adjust the setpoint lower until your desired room temp is achieved.

If it's inconsistent then maybe you need to replace them with something more reliable.

Thanks for replying. It is inconsistant on occaision. When it is set at 68 degrees we will look at sometimes and it will read that it is 74 degrees in the room (it feels hot and that is why we check) and the red light is still on meaning it hasn't shut off raising the heat. So it knows it is above what we set it at. It has happened with the other ones in different rooms. It does fine most of the time but then it pulls that and I wonder how safe they are. I already had the manufacturer replace them but still this happens once in awhile. Do you know of another brand that works well/reliable and has one and two pole units? Also I really like being able to turn the heat off completely which these allow. These were about 60 dollars each. I recall it being kind of difficult to find replacements for the old original thermostats and King Electric was recommended and I think that was the same maker of the old ones. In the early 1980's I got one of the first fancy Honewell thermostats that you could program and that one worked fine. The professor of electrical engineering at local university who bought my little house as a rental was completely enthralled with that thermostat. So would Honeywell be a better way to go? I am open to suggestions.
Thank you for letting me know about the plaster too.

Sometimes there is a setting on the tstat, inside, called cycle rate. Make sure this is at its slowest setting. An air system would need a fast setting, steam heat would need a slow setting. There probably is not a specific setting for ceiling radiant.
There is another setting that might be called "heat anticipator" try screwing around with that. A digital stat might also have a "differential" setting.
If you dont have these setting options available, you might have to buy a more expensive stat.
Another option is to eliminate that stat altogether and run the system on reset control.

Thanks for responding Bill. Well I tried to find such settings on the King Electric thermostat and had no luck.

Do you know of a brand that I should try?

What I still don't understand is if I set the temp at 68 degrees and then I check it and it says 73 degrees and the light is still on and the thermostat still hasn't shut off wouldn't that be something else? It doesn't do it all the time but frequently so we are worried about it being a hazard besides just making things uncomfortable.  I can see where the ceiling heat when it reaches it's set temp will shut off and then it takes time for it to cool down and it could go up some right after it shuts off just due to the fact it is hot and dense and can take awhile to cool down. But clearly it knows it is 5 degrees over the set temp and it still doesn't turn off indicated by the light on the thermostat.

I thought maybe dust got down into it and I have blown on it and when it reads my warmer air it then clicks off. So it does have the ability to re-evaluate even if it is on some sort of slow cycle. I just think they weren't designed for this sort of application even though we were told by the company it would work.

We would be looking for a brand that has one and two pole options as well as the ability to completely turn the thermostat off. We like the digital display and being able to program the temperature, especially with the radiant heat since in the mornings it takes awhile to heat things up and to set it to do that before we wake up is really nice.

Well I looked up the model of King Electic we have they are the ESP120 and ESp230. It says that they are electonically anticipated. It says that it has a 3 min. delay between cycles. It has a thermistor sensor.
It doesn't appear that it can be adjusted and they do say they are designed for several types of applications and one being radiant. It is one of their Premium thermostats but I can say for a fact that the ones we have don't work effectively for radiant ceiling heat. Does anyone have any suggestions on what other brand and model to try?

Turns out the thermostat can be attached to the wrong poles.  If that is the case, the thermostat will turn off when it is set for a very high temperature ...and it will turn on as though it is set for "high" if it set for the lowest temperature.  

It will look like you've turned it way down and it's not actually turning off.  If that is the case, the wiring may be attached to the wrong poles.