Are there any legitimate animal welfare concerns about the way that turkeys are slaughtered to make them halal?
Oh, absolutely. Though, as mentioned above, that's an odd thing for Geller and her group to be concerned about, since halal slaughter is effectively the same as kosher slaughter (at least as far as treatment of the animal is concerned), to the point where, as the article in my OP notes, laws banning halal slaughter make kosher slaughter illegal as well.
Given that Geller is (ostensibly, anyway) Jewish, and often mentions how that is one of the major motivations behind her anti-Islam activism, one would think she'd be a bit more cognizant of how her crusade against halal could have an equally detrimental effect on members of her own religion that just want to follow their religious dietary laws.
Also, what exactly is the process to make them halal? Are they just automatically halal by virtue of not being on a list of forbidden foods, or do they have to undergo some kind of special treatment?
"Halal" simple means "permitted", under Muslim religious law. Sometimes this a matter of simply not eating things that have been forbidden (like pork). In other cases, there are certain things that have to be done in order to make something "permitted".
Slaughtering and butchering an animal so that is halal for Muslims to consume is called
dhabihah. It's supposed to be carried out by a
Dhabih, a mentally competent adult Muslim who understands the rules for halal slaughter (the slaughter itself can be carried out by any Person of the Book, as long as a Muslim who understands the rules supervises the process). The animal, which can't have died of old age or disease or been beaten to death, is laid in the direction of Mecca, the
Dhabih performs an abbreviated
Tasmiyyah, saying "Bismalla allahu akhbar" ("In the name of God, God is the Greatest"), and its trachea esophagus and jugular are cut in a single swift stroke by an extremely sharp knife, and the animal's blood is drained.
The only major difference between
dhabihah and
shechita (slaughter of animals under Jewish religious law so it's kosher) is the
Tasmiyyah - the throat-slitting followed by the draining of blood. To be halal, the animal can
not have had the names of any other gods but God pronounced over it before the slaughter, and God's name
has to be pronounced. In
shechita, God does not need to be invoked.
In neither case is the animal allowed to be bolt-stunned before being slaughtered, as is the usual practice in Western slaughterhouses. There is, however, some dispute as to whether minor electrical stunning is permissible for halal livestock slaughter (though even this isn't permissible for kosher slaughter - that's partly why kosher considered halal, but halal isn't necessarily kosher).
Note that mechanical slaughter of poultry is still controversial, though mostly accepted as long as the birds are not stunned, the machine is operated by a trained Muslim who can perform
Tasmiyyah, and the machine properly cuts the trachea, esophagus, and jugular.