Here are some of the things I have tweaked in my process. I generally concentrated on improving one area per batch until I felt my brews have reached commercial quality (which was after all of these elements were in place):
Sanitation - after use all equipment gets a soak in oxyclean and is sanitized before storing. I rinse equipment and sanitize again with StarSan before use, leaving all equipment in the bucket of sanitizer until it is pulled out and used. I mix 1oz StarSan in 4 gallons of water which is slightly stronger than the recommended ratio. I have found it lasts for 3 weeks, I discard when it starts to turn cloudy. I allow sanitizer to contact my fermenter for one hour before racking the wort since I use plastic. My transfer tubing gets replaced every 10 batches or when I notice it is starting to discolor. All parts which touch beer or wort get broken down and cleaned/sanitized after every brew (racking cane, keg dip tubes, keg O-rings, etc) to ensure there are no voids which could harbor bacteria. I don't use fermenters or bottling buckets with spigots because spigots are very difficult to sanitize properly. When I prepare yeast starters I sanitize the flask and then boil and cool the starter wort in the flask whenever I can. This way I know the starter wort is sterile, not just sanitized, particularly if I plan to harvest the yeast.
Water quality - I slowly carbon filter my tap water and dilute with R.O. water to reach the desired hardness level. I then add gypsum or calcium chloride to the mash to get back to over 50ppm calcium. The calcium not only provides proper mash pH, it is an essential yeast nutrient.
Mash - I don't over-crush my grains (my mill is at 0.036 which gives me about 80% efficiency), I runoff and vorlauf slowly to ensure the wort going to the kettle is clear, I sparge with the grainbed between 165*F and 170*F, and I am careful to maintain runnings below a pH of 6. 5.2 stabilizer is helpful for batch sparging, when fly sparging I add phosphoric acid to the sparge water and check the pH of my last runnings. I try to minimize HSA as much as is practical but I am not psychotic about it.
Boil - I boil very hard, use Whirlfloc to coagulate proteins, and chill using an immersion chiller to get below 140*F as quickly as possible to rid DMS. I keep the kettle covered below 140*F to keep out contaminants. I use a hop strainer to remove hop material and whirlpool/syphon from the kettle to leave behind most break material. This allows for a clean compact yeast cake in the fermenter that will stay behind when the beer is racked to the keg.
Yeast - I pitch a minimum of the yeast recommended by
Jamil's pitching rate calculator. I use yeast nutrient containing zinc in every batch which helps reduce lag time since most brewing water is zinc deficient. I use O2 to aerate with a stone, aiming for at least 20ppm of O2. Shaking a carboy will only get to 8ppm or so.
Fermentation - I pitch at the bottom end of the yeast's recommended range and hold the temp there until visible fermentation, then I maintain temps in the middle of the recommended range until fermentation slows. I use a minimum two week primary, typically I will primary for 3 weeks except on really small session beers. I don't secondary unless I am doing a really big beer because the extra racking is just another opportunity for oxidation and contamination to occur. This goes back to WBC's comments of having a closed system. When I transfer I avoid splashing the beer, I use an autosiphon, and I keep the fermenter and keg covered up as much as possible.
Storage/serving - I use kegs with 1/2" cut off of the dip tube and force carbonate my brews. The exception is beers where bottle conditioning is part of the style -- eg. some Belgians (dubel, tripel, saison). A couple of weeks in the keg before tapping provides ample time for yeast to drop out, leaving a crystal clear beer. Bottle conditioned beers, no matter how carefully handled, always have some residual yeast which gives a yeasty flavor and clouds the brew. Unless you are trying to emulate a cask-conditioned beer, I really think force carbonating in kegs is the way to go, and it makes a huge difference in the perception of the brew. (I have had folks over who said they never liked homebrew before mine because it was always "yeasty") If you do have to bottle condition, you can do what some German breweries do: use finings or filter to drop the ale yeast out, and add a lager yeast at bottling time. Then allow to carbonate at 50*F for 3-4 weeks. The lager yeast will not remain in suspension in the bottle like an ale yeast will.
Hopefully some of this helps.