As a biologist, I feel compelled to point out that two of the organs offered as vestigial are not actually recognized as such today.
The sacrum serves at least two vital functions. First, the sacral nerves need to exit the spine below the juncture of spine and pelvis to innervate the buttocks, legs, and other *ahem* important *ahem* organs. Without the sacrum descending below the rest of the spine as protection, these nerves would be much more prone to damage and paraplegia would be correspondingly more common.
Further, the structure of the perineum necessitates an attachment point for muscles which might be regarded as "important" (defecation would be either impossible or "automatic" depending on which muscles were detached) and *ahem* important *ahem*. The coccyx, which articulates with the distal end of the sacrum, provides these anchorage points.
The appendix serves at least two known important purposes. First, it is one of the densest patches of immune tissue in the human gut. Gut-associated lymphoid tissue (GALT) is one of the first lines of defense in the body, as the gut is the system most exposed to the outside world (What? You thought it was the skin? Nope. Skin cells are protected from direct contact by a thick armour plating of dead, keratinized cells.) and thus most often exposed to pathogens. GALT both produces and stores the immune cells which respond to potential pathogens.
The pocket-like "dead end" structure of the appendix allows it to capture small amounts of matter as digestion proceeds and "examine" it for longer than most other GALTs. As generation of "matching" immune cells is a probabilistic process (immune cells are generated at random and ones that find a "matching" pathogen proliferate), this "lag time" assists in the detection of and defense against pathogens.
As well, the fact that the contents of the appendix are only slowly "turned over" and replaced makes it a haven for essential gut flora ("good germs") in case of catastrophic (from the gut's perspective) events such as diarrhea which flush most of the flora from the gut.
For these reasons, people with intact appendices both suffer a lower incidence of gastrointestinal infection and recover from such infections much more quickly.
While no studies that I've been able to find — granted, in only about fifteen minutes of searching the literature — seem to deal with the consequences of a missing palmaris longus muscle, it may contribute (like other weak muscles which work alongside stronger muscles) to stability rather than to strength. I'll leave that for those who could actually research it, though.
If you still think the sacrum is vestigial, though, I'll remove yours for you.