Where to begin?
The most important aspect of the Montauk Project is, of course; "Does this fit into my campaign?" Most superheroic universes and settings can quite easily accept the idea that the US Navy may have been involved with some form of secret experiment designed to help win the World War II. In fact, the Navy was involved in various secret experiments, dealing with everything from planes to torpedoes. So making the initial Philadelphia Experiment a "real world" event isn't all that difficult. Naturally, the GM will need to decide if the Experiment worked exactly as described or if the "facts" have become confused over time.
Once the validity of the original Experiment is established, the next step is to decide which elements of the rest of the Project history can be adapted to a super hero (or other genre) campaign. Depending on the particular universe, some of the details might need to be altered in order to reflect the GM's particular tastes. For example, much of the initial funding of the Montauk Project is said to come from 10 billion in gold smuggled out of Europe by remnants of the Third Reich. If a GM tends to shy away from using Nazis or Nazi-inspired villains in his campaign then the source of this gold may need to be changed. The same goes for the the ITT World-Wide Communications Corporation said to be owned by the Krupp family. If the GM wishes to avoid Nazi involvement, then this company should be changed as well. If using a universe similar to the established HERO Games Champions Universe then the source of the 10 billion in gold and the owners of ITT World-Wide Communications is simple: VIPER. Much of the technology said to be developed by the Montauk Project (such as time travel and mind control) has the perfect "super-science" feel commonly found in plots dealing with VIPER. Besides, what criminal organization couldn't resist developing technology that would allow them to manipulate time, know what people are thinking, scout a remote location safely, and control what their foes think and do?
Other groups and individuals from the Champions Universe that could be used in relation to the project include Dr. Destroyer (obviously operating through a false front), Istvatha V’han (the entire project becomes an attempt to open a permanent gate between Earth and V’han’s world so she can launch a full-scale invasion), the Warlord (although the scope and nature of this project seems far beyond what he usually attempts), PSI (who’d be especially interested in the mind control aspect of the project). Of course, the GM could work with the material as written and make the people responsible rogue elements of the military, the CIA and the NSA (a.k.a. the National Security Agency a.k.a. “No Such Agency”).
The next question would be alien involvement. If the GM doesn't use aliens in his game then these elements could be simply discarded (even the author states that such involvement is only "rumor"). If he does use aliens, the question become much more interesting. The book lists two groups: the Orions and the Sirians. The Sirians are said to come from the star system of Sirius, while the Orions are simply described as coming from the constellation of Orion. No other facts are given, giving any GM free reign to develop them any was he see fit. If aliens are a known quantity in the game universe, then the GM needs to determine if the aliens responsible are ones he’s already established, or ones new to the campaign (or, at least new to the PCs). Even if the aliens are members of an established race, they could always be "rogue" members of that race, supplying the technology for reasons known only to them.
Aside from interstellar aliens, there is also the question about Mars. Does the GM want large artificial structures littering the surface of the planet? If so, who made them? Martians, or other aliens? The book states Duncan had to search 125,000 years in the past to find any evidence of life on Mars. Thus, the GM could presume the artifacts were either built by Martians, or some other race who happened to be passing through the solar system. For a real twist, the structures on Mars could have been built by humans. Either an advanced race from Earth (now long gone), or a race of beings who eventually settled on Earth (a popular theory seen in such shows as Battlestar Galactica and hinted at in the game Doom 3). If the GM goes with the former idea, the connections to the Atlantis mythos (and the Egyptians and their pyramids) are obvious.
Of course, there is the question about what to do with the "The Solar System Defense" said to be on Mars. it’s likely the such a device could be ignored by the GM in favor of his own theories and plots. What ever is within the pyramids of Mars, however, it should be some sort of highly advanced (and very dangerous) technology.
The last question a GM needs to consider are the claims that the people involved in the Montauk Project manipulated time. Of course, a clever GM may decide that anything the Montauk researchers did to the past has already happened, thus the PC's accepted past is the result of Montauk Project manipulations. Now, as for sending people two to three hundred years into the future (or the dead city of 6037 AD) once can always take the "alternate time" angle. The futures seen by the Montauk researchers may not be the future, but simply a future.
Possible the biggest question surrounding the entire project (especially the latter parts dealing with the manipulation of time) is "Where did all the test subjects come from?" Looking over the numbers given in the book, it would seem that at the very minimum the Montauk Project sent several hundred people to various time lines. If the Project was kidnapping homeless people and large numbers of young children (not to mention the "between 3000 and 10,000 people" sent into the future) someone would be bound to notice (we hope). Even in a city as large as New York, the disappearance of a large number of homeless would probably be noticed, especially when you realize that the time tampering portion of the experiment only lasted for three years—from 1981 to 1983. Add in the quantity of young children hinted at, and the number of people possibly involved is staggering. Such a situation makes an excellent hook for PCs to get involved. Of course, if the PCs are based somewhere else other than New York, then the the disappearances may have gone on unopposed, with the PCs possibly forced to recover the temporally lost people.
Finally, there is the question of what to do with Montauk Base. Is the Project still operating? Did, in fact, Duncan Cameron rebel and summon the Beast to destroy the base? Did the Project reestablish itself somewhere else? It would make sense that the technology developed during the course of the Project is being used else where (possibly by the high-tech criminal organization of the GM's choice) and that the Base was abandoned as described. In that case, the PCs may explore Montauk AFB and Fort Hero only to find it’s closed down and abandoned, with clues pointing to a newer base established elsewhere in the world. The possibilities are only limited by the GM's imagination.