Nose mounted machine guns and cannon.

[Charlie_c67]

Or they should've done in the case of the MiG-9...

[Andrew Gorman]

Jets with center mounted guns and nose intakes had problems ingesting ammunition fumes- it was a problem with the Mig-9, and led to some weird work arounds, like the intakes on the Il-40-
https://en.wikipedia.org/wiki/Ilyushin_Il-40

[Charlie_c67]

Yes that aircraft always makes me think of Errol from the Discworld series 

[Rick Lowe]

Yes that aircraft always makes me think of Errol from the Discworld series 

Nice reference - and yes, I agree. 

[NARSES2]

Yes that aircraft always makes me think of Errol from the Discworld series 

  

[Weaver]

On synchronisation, another issue is that it generally reduces the rate of fire of the synchronised gun by anything up to 10%. Given that the whole point of the RAF's eight-gun policy was to get as many bullets down range as possible in the shortest time, it would have been counterproductive to lose some to synchronisation. 

Spread and number of guns. Wing mounted allowed more guns and a greater probability of hit but less damage.  Nose mounted allowed greater concentration of fire and more damage but a lower chance of a hit. Pros and cons to both.

Nose mounted may also increase the drag slightly.

Centreline nose-mounted MG and cannon have a higher probability of a damaging hit than spread out wing-mounted guns because deflection shots are much simpler with that layout. Wing-mounted guns have to be adjusted to converge at a given range, if the target is at exactly the right place the massed fire is most effective, inside or outside of the sweetspot means that the probability of a killshot drops, especially with rifle caliber ammunition i.e. .303, .30, 7.92 etc. Deflection shooting is also more difficult than with nose mounted armament. Which is one of the reasons why wing-mounted cannon armament became more common, over or under was less of an issue. The USAAF was the only airforce that stayed with an MG only armament for various reasons, primarily logistics in spite of claims that six to eight .50 was just as effective as cannon because of weight of fire. The reality is that with thousands of bombers and fighters in service all using the same ammunition the logistics trail was much simpler from factory to field if they stayed with the .50 M2. The USN however made the move to cannon later in the war, they wanted to be sure they knocked down the target. Also as the USN logistics train was very different swapping out .50 for 20mm wasn't as much of an issue and the USN was already used to sourcing and handling a broader range of ordnance.

As to synchronization it isn't that difficult even with the larger more powerful engines of the period. The Germans had the best approach, they used electrically ignited ammunition, the primer flashed when the circuit was closed.

Spot on. Also:

USAAF fighters were predominantly fighting German fighters, which were hard to hit, rather than four-engined bombers, which were hard to destroy. Six or eight .50cals were better for this application because the large number of guns gave them a better statistical chance of a hit, and the .50cal's higher muzzle velocity gave them a better ballistic chance of a hit. They were also doing this in a war of attrition where the stakes, the loss of one friendly bomber, were small compared to the force size.

The USN were already buying large quantities of 20x110mm ammo for their deck-mounted Oerlikon guns, so putting cannon on their fighters was less of a logistics burden. They were also encountering Japanese bombers, which weren't super-tough, but that might change at any moment. The real issue though was that they were fighting a war where the stakes, the loss of an aircraft carrier to a single bomb or kamikaze, were large and consequential compared to the force size. That made taking down that one aircraft heading for the carrier as soon and as surely as possible very, VERY important.

It's a bit like the situation, thirty years later, where the USN's F-14 carried Phoenix and the USAF's F-15 didn't. The potential loss of an aircraft carrier was the only thing that justified million-dollar-per-shot-missiles on the defending fighters.