I'm basically familiar with the term open and closed bolt design but what exactly are the pros and cons from an engineering or manufacturing standpoint? Which is better for specific weapon applications or designs? Are there legal issues involved with open bolt designs? Are there caliber/energy issues with one systems over another?  I know this has probably been talked to death but I see these terms tossed about in gun books and magazines and frankly I just feel a bit ignorant not being in the know.

Normally I equate "open bolt" with full auto type weapons.

In operation when you retract the bolt and release, the bolt stays back until you pull the trigger, then it slams forward picks up a round, goes into battery, fires and returns. After you release the trigger the bolt will still be in the "open" position.
I think? there are some semi-auto weapons that do fire from an open bolt.

"Closed bolt" means when you retract the bolt and release, the bolt slams forward and picks up a round and locks into battery. Requiring you to operate the trigger. Most semi-autos are "closed bolt" guns, however ther are some (generally modified full autos, like Uzi Model "A"s) which fire from closed bolts.

Accuracy is generally perceived to be better w/ "closed bolt" type weapons.

The main reason for open bolt action is that with fully automatic weapons it prevents the cookoffs and aids in cooling, especially important in machineguns. Most older SMGs are open bolt since it was cheaper and easier to manufacture.

As mentioned, open bolts help prevent cookoffs, in which the cartridge is fired because of excessive heat in the chamber. So it's mostly a full-auto thing.

It's very difficult to sell an open bolt design in the US. They're regarded as easier to illegally convert to full-auto.

All else equal, the only accuracy difference between an open bolt and closed bolt gun is on the first round in a burst.  This is a result of the jarring action of the bolt lunging forward when you pull the trigger on an OB.  On a CB, when you pull the trigger, there is no such action to throw your aim - only that of the hammer dropping.

As for legalities, in 1981 BTAF ruled that open bolt guns were too easily converted to machineguns and thus classified all open bolt guns made after that date to be machineguns, regardless of whether they will fire more than one round per pull of the trigger without manipulation or modification.  OB guns made before 1981 were to be grandfathered.  In 1996 (or maybe it was 1998) US v. Cash (a 7th Circuit case on unregistered DIAS's) seemed to indicate that BATF did not have the regulatory power to grandfather certain weapons as not covered by the NFA because they were made prior to a BATF ruling while classifying other identical weapons made after the ruling as NFA weapons.  Thus, while BATF has not pushed the issue, there is some question as to the legality of any OB weapon, regardless of when manufactured, if it is not registered as a machinegun...especially in the 7th Circuit.