The rubbery effect is caused by skin filler injections used to alter the overall size and shape of the face.  Sometimes the effect is fairly realistic, and sometimes it is just bizarre: 

The fillers can run out in a matter of hours causing sagging and finally a "deflated" appearance. 

Please see Faul's Underskin Filler Duration Documentation

It's not unusual to see him playing with his rubber cheeks, just try doing the same with your own face, you can't unless you have some synthetics under your skin:

Here's a very bad effect on the chin:

Also this sequence of shots from Faul and Linda's wedding is another good example of a bad skin filler effect.
Btw, it's too bad every celebrity impersonator can't marry a professional photographer

Hey, Jude, don't be afraid
You were made to go out and get her
The minute you let her under your skin
Then you begin to make it better.

I don't rule out the possibility of shapeshifting, but in my opinion that is NOT what is happening in his case.  But it would be interesting to see how many people prefer to believe instead that these wild effects on his face are caused by shapeshifting, and would say it is insane and deluded to suggest that sometimes humans simply impersonate other humans.  I only make that comment because the level of defensive I have encountered in people about this topic is absolutely over the moon.

The use of skin fillers is one way to dramatically alter a person's apperance temporarily.  Oh yeah, did I forget to mention once again the prosthetics...

Faul and his rubber nose collection

Were you talking about this photo?

It's just a disguise, and the photo is reversed.  It is highly doubtful that this was his original look.

Perhaps this was close to his original appearance...

http://digilander.libero.it/p_truth/the … pepper.gif 

Phil Ackrill (also known as Phil Ralston) of Denny Laine and the Diplomats (third from the left)

Please note Mary McCartney's resemblance to Phil:

Stella and James both have reddish-blonde hair so maybe this was also their father's true hair color.

After leaving the Diplomats, Phil/Faul's first role with the Beatles was that of Neil Apsinall, tour manager:

NEIL ASPINALL ------------------------------------------------------------FAUX PAUL MCCARTNEY

http://60if.proboards21.com/index.cgi?b … 1128761138

Neil bears a strong resemblance to Phil Ackrill as well:

It is really unclear what his original (birth) identity was, if indeed he was ever allowed to have one.