Generally it is presumed that a rolling start from the taxy will provide an acceptable outcome.
For acceleration from static,
(a) the low weight case is more of a concern as the breakaway thrust required is lower .. ie the aircraft will be expected to have travelled some distance prior to finally having the thrust set correctly.
(b) for weights approaching gross, the breakaway thrust is higher and, for the same time allowance to set thrust, the aircraft will have travelled a shorter distance .. in my experience, prompt pilot action sees takeoff thrust set in the first few feet of travel at heavy weights.
Re the specific comments .. pilot technique has to be prompt without needless dilly dallying .. spin up and then push the levers up (or use the button) .. should only take a couple of seconds. A pilot who takes a long time really needs some corrective training, methinks.
Rolling takeoff should not be a problem .. as the aircraft approaches the runway heading, the engines go to spin up and then to the required takeoff setting. I can't recall any problems on the line for the 727/737 .. perhaps it is different on other Types ?