One last suggestion, I promise. . .
Oliver Hudson (Rules of Engagement).
I don’t think Joseph Fiennes, star of Shakespeare in Love, was miscast: http://handson.provocateuse.com/images/photos/joseph_fiennes_01.jpg
I’d like to see the picture that makes Tim look like Billy.
Do you have another picture? That link is forbidden to me.
Try these:
http://storage.people.com/jpgs/19990510/19990510-750-144.jpg
http://www.theglobalstrongtrust.com/files/imagecache/product/files/joseph-web.jpg
http://www.noos.org/mecs/joseph/jseph1.jpg
Much better. And Joe’s definitely in the running.
Have a thing for Joe, huh? 
If this is supposed to be the most authentic (realistic?) portrait of Shakespeare made during his lifetime, how do they know? How do experts determine this? I would think a more flattering portrait would be less likely to be authentic.
Not particularly. I just like fishing around with Google Images. I’ll just as happily do so (and have, on these very boards) for pictures of Keira Knightley or Missy Peregrym. 
Sorry to be so late responding. Meant to earlier.
I’m not proposing that anyone will be cast by looks alone and certainly not by age proximity.
This is meant to be a search for a look-alike that can be corroborated by a link to a picture (or more).
Alan wouldn’t get the role for another reason: he looks too mean, and the baggage he would bring would smack too much of the villains he’s played. He has done some sympathetic roles, even those where his sensitive side is out front, but I think the casting types would have his age somewhat down the list of why he wouldn’t get the job.
Just my opinion with which you are free to disagree.
That’s the motto of IMHO. You’re in CS. 
No, that’s how I treat SDMB, and why I stay away from Facts Only places.
Yeah, I was under the impression that we still don’t really know what he looked like and that all supposed portraits of him are at the very least posthumous and unverifiable, if not downright fictions.
With a heavy dose of wishful thinking.
No, seriously, there are several ways of making such identifications.
Comparison with other known images, possibly of a later date. In the case of Shakespeare, there is the frontispiece of the First Folio and the bust on his memorial in the church at Stratford. Both of those were probably produced after Shakespeare’s death, but they would have been commissioned by people who had known him well and quite possibly used existing portraits (which might since have been lost, but, then again, might not). In fact, one of the most common ways seventeenth-century portraits are identified is from engravings, including frontispieces, as such engravings are much more likely to have the person’s name on them.
Or evidence that a particular portrait originally belonged to someone related to or associated with that person.
Or an early tradition that a particular portrait represented that person.
Or, as was common on portraits of this period, the painting does not say who the painting is of, but does gives the date and the sitter’s age, thereby (slightly) narrowing down the range of possible identifications.
Or the manner in which the person is portrayed is relevant to that particular person. Does it allude to a significant event in that person’s life? Or their job? Or their name?
In this case, the claim is that it vaguely resembles the frontispiece, that it may have some (seemingly not-yet-specified) family association with the Earl of Southampton, Shakespeare’s patron, that at least one copy of this portrait was later believed to show Shakespeare, that that copy had the right age on it (albeit added later) and that the motto on the painting could imply that the sitter was a playwright. None of which seem to me to be more than slightly interesting. But those are certainly the types of arguments that, in other cases, can be used to make plausible identifications.