Am servicing a unit some one used to service before the technician told the owner do not turn off the thermostat so it run all night long and on weekend too.is it right or should I put a programmable thermostat

Depends. What is the application? Is there a lot of humidity in the area? Is this for the blower only or the furnace OR A/C.

The system is a a/c unit

Are you talking about running the blower continuously or the air conditioning?

If you run the indoor blower all the time in A/C mode you will introduce some of the moisture back into the house you just paid to remove.