I have used synthetic oil in my cars since 1980. Synthetic oils will not cause oil leaks or an engine to burn more oil, on the contrary, an engine that tends to burn oil will burn less with synthetic due to the molecular structure of synthetics (all the molecules are uniform in size, petroleum based oils do not have a uniform structure). The above comment is correct regarding oil leaks - if the engine's sealing/gasket system is sound, then synthetic oils will not cause them to leak. However; if there is already wear or deterioration and leaks that have sealed themselves over time due to dirt buildup, then synthetics will naturally clean away the dirt, thereby exposing the leak, but not causing the leak.
As far as putting synthetic oil in a brand new engine (before break in) there is conflicting information. Some say that due to todays better machining tolerances, that putting synthetic oil in right away will not prevent rings from seating properly. Others say that synthetics are too slick to use in a brand new engine and the rings will not seat. If you are worried about this, then run a petroleum based oil for 500 or so miles and then switch to synthetics.
The advantages are well worth the extra cost - less friction which means lower oil temps and better gas mileage. Synthetics clean better and do not break down under high heat conditions like petroleum oils and synthetics have a much lower pour point (well below 0 F).
