Just picked up an '04 Silverado Z71 last week, 35600 miles on it. I LOVE THIS TRUCK. But as minor as it may seem, there's a slight thump intermittently in the tranny area. I can feel it in the pedal when it happens, usually when going up a hill after a few seconds in 3rd, or after letting off the gas completely going down a hill.

A buddy told me someone he knew had the exact same thing happen, and the dealers couldn't figure it out, and that nothing ever happened with the tranny. Just wondering if anyone else has run into this?

 

The thump may be one or both of two things.
The First; There is slack in the yoke where your tranny meets the driveshaft. The Dlrshps know of this problem but unless you produce the TSBs (yes there are more than one), you will get nowhere. If this continues, you have the chance of either snapping your shaft at the rear U/joint or taking out your rear end completely. If your rear end goes out first, which may very well happen, you need to contact GM Customer Complaint and explain that you have made every effort to get the Dlrshps help and they have played nothing but dumb. GM will get you to another Dlrshp which will replace the rear end as well as replace the driveshaft.
If the driveshaft goes out first, consider yourself lucky. You more than likely will never have any rear end issues. Again, contact GM Complaint if your Dlrshp refuses to help and they will. What I would strongly suggest is you bring this to the attention of GM anyway now before any damage at all happens.
The Second; Also know that what you may feel could be the Sun Gear in the Tranny. I have told others this so I will suggest it to you. Contact another Transmission shop outside of a GM dlrshp. Try "AAMCO," and ask them about the Sun Gear breakage / weakness and advise of symptoms you have described here. You may be able to save your Tranny and your wallet. I know that AMMCO charges $800 to repair this problem. A New Trans will run you about $3000. Get some advise sooner than later.
GL - Greek
Here are a Few TSBs for your year, maybe your problem.
1.) TSB #3105C -- PING, POP, SNAP, OR CLICK NOISE FROM THE PROPELLER SHAFT. *SC (NHTSA ID #10009978, no date provided
2.) TSB #050730017 -- 4L60-E/4L65-E AUTOMATIC TRANSMISSION/TORQUE CONVERTER CLUTCH (TCC) SHUDDER, WATER IN TRANSMISSION. *TT (NHTSA ID #10017462, FEBRUARY 01 2006)
3.) TSB #04222004 -- RATTLE TYPE NOISE DUE TO A CRACKED FLEX PLATE. GM VOICEMAIL EXPRESS. *TT (NHTSA ID #10009235, APRIL 22 2004)
4.) TSB #020730024A -- DIAGNOSIS OF CRACKED OR BROKEN TRANSMISSION CASE. *TT 2006 AND PRIOR CARS AND LIGHT DUTY TRUCKS. *TT (NHTSA ID #634999, AUGUST 01 2005)
5.) TSB #3300 -- 4WD MODELS WITH NOISE, VIBRATION ON DRY PAVEMENT. *EH (NHTSA ID #10013572, no date provided)
6.) TSB #01654 -- SQUAWK OR GRUNT NOISE THAT OCCURS ON THE 2-3 UPSHIFT ON VEHICLES WITH 4L60E - M30, 4L60E M32 TRANSMISSION. *TT (NHTSA ID #10007233, JANUARY 01 2004)
7.) TSB #00702 -- SLIP CONDITION IN 2ND, 3RD OR 4TH DAMAGED 2-4 BAND 3-4 CLUTCH ON THE 4L60E/4L65E AUTOMATIC TRANSMISSION. *TT *MJ (NHTSA ID #10005476, JANUARY 01 2004)
9.) TSB #3364 -- REAR AXLE RETAINER BUTTON BREAKAGE. *EH (NHTSA ID #10014953, no date provided)