The two revisions in weapon specialization are in
PHBR1 The Complete Fighter's Handbook page 58:
"
Only single-class warriors (fighters, paladins, and rangers) can take weapon specialties. Such a character can only take one when he is first created, but may specialize in more weapons as he gains new slots."
On page 35 under swashbuckler kit it mentions multiple weapon specializations as a requirement of the kit:
"Weapon Proficiencies: The Swashbuckler receives two extra weapon proficiency slots which must be devoted to weapon proficiency with one of the following weapons: stiletto*, main-gauche*, rapier*,and sabre*. (The " * " symbol denotes new weapons to be found in the Equipment chapter.)
Throughout his career, he must devote half of his weapon proficiency slots to those four weapons. Once he has achieved specialization in all four of those weapons, he may freely choose where the rest of his weapon proficiency slots go."
Wow, how did I never notice that? That's wild, especially when the Dark Sun Gladiator grants the ability to specialize in multiple weapons as a class feature. And they just handed weapon specialization to Rangers and Paladins, too? All this time, I thought only certain Kits would let me do that...
However, it seems there was some contention about this in-house at TSR, which is why later books don't support this. In fact, in Sage Advice, they had this to say:
"Q. The Player’s Handbook, on pages 26 and 52, makes it clear that only single-classed fighters, not paladins and rangers, can use weapon specialization. However, the Complete Fighter’s Handbook, on page 58, pretty clearly implies that all warriors (fighters, paladins, and rangers) can specialize. Did the rules change when the Complete Fighter’s Handbook hit the shelves? If so, why would anyone want to play a simple fighter?
A. According to a short conversation I had with TSR, Inc.’s Dave "Zeb" Cook a while ago, the rules in the Player’s Handbook and Dungeon Master’s Guide are intended to serve as the fundamental basis for the AD&D® 2nd Edition game and are supposed to remain unchanged until that far off day when a new version of the game comes along (there are no plans for another edition currently in the works, but no set of game rules stays current forever). While there is a continuous stream of new material planned for the game, all of it is intended to supplement the core rules, not replace them. All of the rules in the Complete Fighter’s Handbook are optional,
but the phrase giving weapon specialization to all warriors is an error."
However, then we have:
"Q. With how many weapons can a fighter specialize? Is it possible to specialize in both a fighting style (from the Complete Fighter’s Handbook) and a weapon or combination of weapons? How do you use weapon specialization if you also are using weapon groups from the Complete Fighter’s Handbook? Is it possible to double specialize? If so, how do you get it and what bonuses do you get for it?
A. In the core rules, a single-classed Fighter, and only a fighter, can specialize
in exactly one particular weapon. If you’re using weapon groups, the fighter must pick one weapon within the group as a specialty.
If you’re using the rules in the Complete Fighters Handbook, you can allow fighters to take more than one weapon specialization, but they still must choose their specializations one weapon at a time.
Style specialization is actually just a weapon proficiency available to warriors, rogues, and priests. Don’t let the name confuse you; a style specialization is a general set of tricks for fighting a certain way, not an intensive study of one particular weapon. It is possible for a character to have more than one style specialization.
There are no rules for double specializations in the current version of the AD&D game. However, if you play a variant game and allow all warriors (including rangers and paladins) to take weapon specialization, you might allow fighters only to spend two extra proficiency slots on one weapon (and one weapon only) and become double specialized. The effect of a double specialization is up to the DM, but increasing the specialization bonus to +2 ’to hit’ and +3 damage seems most reasonable. If you use this unofficial optional rule, be prepared to start adjusting your campaign’s play balance, because your poor monsters are going to have a hard time going toe-to-toe with your campaign’s fighters."
Clear as mud, lol. Apparently since all the Complete Books are "optional", you can use them and allow multiple specializations to Fighters if you want to, but that's not ever going to be in the PHB...???
(And supposedly they cleared this up in the 9th printing of the CFH, though I have no way to confirm that).