I just had a new deck built, only to discover that one section of it isn't
level. It's out by 1/2 inch over a four foot run.

Is this acceptable and within reasonable tolerances? Or should I withold
some of the payment to the builder? If the latter, how much should I
penalize him (as a percentage of the total)?

Beebo... some good news.

A deck is "not" supposed to be level. I've built a ton of decks over
the last 30 years and the rule of thumb is they "must slope away"
from your house.

A deck is an outdoor extension of your indoor living space, and NEEDS
to slope away from the house to allow any water that collects on the
deck to drain away from the house and the foundation of your home.

The amount of slope / angle varies between builder but 1/2" over four
feet is too radical for my taste. The reason is... if your deck
"really does" drop 1/2" every four feet you will physically be
able detect the slope. In other words, if you have your back to the
house while standing on the deck, you will be aware that your toes are
lower than your heels. Like you're walking down an incline.

Here's the deal. At a minimum, the slope should be at least 1" of
slope (drop) for every 15 feet of deck. Among deck builders most follow
a rule of 1/4" for every 4 feet of deck. Just food for thought;
according to Illinois Code, exterior decks require a minimum is 1"
per every 10 feet! (Which equates to 1/2" every five feet.)

Before panicing, your best bet is to double check the "overall" slope
before calling your builder. The easiest way is to use a line level (a
string with a string bubble level)

String level example:
http://www.thenatives.net/edusec3_files/image017.gif

Secure one end of the string to your deck at the house. Stretch the
other end of the string to the edge of your deck. Raise the string
until the bubble is level then measure how far the string is above the
surface of the deck. You can then divide the deck distance by the
height the string is above your deck to calculate your overall drop per
foot. (You can get a bubble level for a dollar at Home Depport)

Like SQlit suggested... approach your deck builder calmly and
professionally. The reason for saying this is if the deck is out of
tolerance, if you push too hard, rather than fix it he could push back
saying the drop is within his tolerances.

Just FYI... I build all my decks to slope 1/4" for every four feet.

Hope this helps
Elton