Q: clicking noise when running on 2003 Infiniti FX35

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Just had a motor mount replaced because of an oil leak they drained the oil but did not put it back soon enough and they say it is slugg build up thats causing in clicking noise when car is cranked the noise is coming from the front near the belts
(1) Answer
Drained the oil? Did not put it back soon enough?

Did they run the engine without oil somehow?

Your concern sounds like an internal engine noise. I would try an independent repair facility to have a technician observe what you are experiencing and give you guidance.