What does "a slip twixt the tongue and the wrist" mean ?

I've never heard that one; it isn't a standard English phrase. It may be a one-off invention. Can you supply some context please?

It seems to be modelled on a well-known proverb "there's many a slip between cup and lip" (which means roughly "there's always a possibility of something going wrong between the beginning and the successful completion of an action").

A logical meaning might be "there's always a possibility of something going wrong between promising something [the tongue] and putting it into action [the wrist]". Does that seem to fit the context in which you found it?

I thought it was a bit unusual too, being familiar with the traditional saying. Then I googled it. Amazingly there are many references to it. I think you're right though syntinen.

Perhaps it's a manifestation of the ability of modern technology to replicate and distribute an error with stunning rapidity.

One of the corrupted sayings that drives me up the wall (irritates me) is the tendency for some to urge someone "don't hide your light under a bushel!" I want to ask "a bushel of what?"

well, in that case you'll have to blame Jesus, who said in Matthew 5:15: "Neither do men light a candle, and put it under a bushel, but on a candlestick." He didn't say what it was a bushel of!

The sentence came from following conversation in the TV show of The West Wing

JOSH：It's gonna sail, Donna.
DONNA：There's many a slip twixt the tongue and the wrist, Josh.
JOSH：Yes. Well, your fortune cookie wisdom notwithstanding, it's gonna sail.
DONNA：Please don't get your hopes up.

Don't let your mouth write a check that your body can't cash.

In most translations it is "basket"

But in the King James translation which was published 1611, it was "bushel". And until the 2nd half of the 20th century that was pretty much the only translation of the Bible that any English-speaking Protestant had access to. So it's natural that people use that version as a proverb.

One definition of "bushel" is a container with a capacity of one bushel (also referred to as a bushel basket).

My secular education is showing.

If you can love someone "a bushel and a peck", surely you can hide your light under a bushel.

Of course if the light is bright and the bushel is old you might--most immodestly-- set the basket on fire.