Starting water temp?

I have been cooking for years. A lot of recipes say that you are supposed to start with cold water if you are making, for example, a stock, or anything where you are cooking something in the water.

For doing a partial boil extract, is there any reason to begin the boil from cold water, or is it okay to use hot water out of the tap to get it up to temp quicker?

Well, I think I've always heard to use cold tap water because of the possibilities of the hot water leaching things out of the pipes, not because it was necessary for what you were cooking. So, if that's the case, then I would also start with cold water for brewing.

hot water heaters build up all kinds of crud inside, including mineral and scale deposits.

if you had one of those tankless water heaters, it'd be ok to use that water.
otherwise, cold tap water, just like cooking. because honestly, making beer IS cooking, with fermentation to complete the recipe.

"Inside many homes, water pipes are made of copper and are bonded together with lead solder. Because the use of lead solder was only banned in the US in 1987, millions of US homes contain lead-soldered copper pipes—and hot water can cause the lead to leach out from this solder. Accordingly, one should avoid cooking with hot water. Also, concerned consumers can "flush" standing water out of the pipes and down the drain, for at least thirty seconds to a minute, prior to using it for cooking or drinking purposes. (This "flushing" method should be applied for an even longer time period when a consumer lives in a high-rise, or whenever water has to travel through greater lengths of pipe than what one would generally find in a typical free-standing home. Also, it is important to note that if there is lead leaching out from the service lines, flushing may require several additional minutes to effectively drain the lead-contaminated water from the system."
http://www.nsc.org/issues/lead/leadinwater.htm