My Peugeot is idling at 1500 revs after having the cylinder head as well as the rings done. what can be the cause?

Agree with Steve P. Possible vacuum leak.

indicates failed valve stem seals
when idling the vacuum in the system sucks oil past the seals down the valve stems and into the cylinder inlet ports behind the valve heads
on acceleration that small amount of oil is allowed into the cylinders indication blue smoke on take off
Blue smoke on hard acceleration is an indication of worn bearings as the bearings are pressed ******* the crank pin, enlarging the clearance on the other side which allows excess oil up onto the cylinder walls which the oil rings cannot control

Carry out a compression check on all cylinders to see if thats shows a fault. If its nil or low, check valve clearances and then head gasket.

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Blue/grey normally means your car is burning oil, could be head gasket or cylinder/rings......be careful of car going into high revs.

industry standards for compression is no more than 10% between cylinders which makes the 90 lb/sq" should be 117 at worst.. If the head job was done properly then a replacement engine is indicated as there is a ring problem in the low cylinder. Rough idle is an indication of a vacuum leak and if the brake booster is not assisting I would be looking at a leaking hose connection between the manifold and the booster Idle rpm is around 900 for a mazda. Check for faulty pc valve allowing excessive air from the sump and not shutting off correctly.

is there smoke coming out of the exhaust? if so what color? if it has white smoke is usually a blown head gasket. if it is a bluish gray it is oil. check your radiator when it is cool. if it appears to have oil in it it could be a blown head gasket. if you leave the radiator cap off start the motor, if you rev the engine and coolant shoots out of the radiator (compression from the cylinder forcing water out) it is a blown head gasket. this can cause the motor to run weak and idle rough and oil to disappear.
if you happen to have a compression gauge take out all of the spark plugs look at the spark plugs if they all look the same or is there ones that look black and sooty(running rich) or looks green(burning antifreeze/water) white Burning hot) http://www.dansmc.com/spark_plugs/spark_plugs_catalog.html
check the compression of each cylinder it is easier if you have an assistant for this. place the gauge over the spark plug hole crank the motor once or twice. the gauge should be around 120 psi (pounds per square inch). if all of the cylinders are under 120 psi more than likely you have worn or broken rings which will cause low compression causing it to run weak and consume oil.

This problem is caused by the injector which the wire for the rev counter pick up comes out of. Check your injectors then remove the one with the wire coming out of it clean and replace. If this doesn't sort both rev counter and knock get a replacement injector. I did this job a few months ago a little bit of stripping down is required but there were no real gotcha's apart from the injector needing to be put back in the head very tightly to prevent fuel leak. Hope this helps.

Its almost certainly the thermostat.

Could be head gasket or piston rings. Piston ring issues will smoke under load or when revving the engine.

Do a compression test.