I finished Papazian's book The Complete Joy of Homebrewing last weekend and learned that a vigorous boil is necessary to isomerize the alpha and beta acids in hops which makes these bittering acids soluble in water-- both the boiling temperature and the physical action of the boil are mechanism by which the hop acids under go isomerisation.
I've also learned on this stackexchange that Dimethylsulphide is boiled off during the boiling period. Leaving a lid on the pot or a lid partially on the pot to help boiling will ultimately lead to some of the DMS condensing on the lid and falling back into the solution, leaving off flavors behind.
Well, I'm starting my first all grain today and my stove just doesn't have the capacity to boil 6.5 gallons of wort beyond the most pathetic boil.
This leads me to ask -- which is worse, boiling with a lid partially covering the pot, therefore increasing the vigor of the boil (substantially), but also increasing the DMS in solution, or boiling with a very weak boil?