I asked this question once again on the Don Bluth Films Facebook page, and this was their response:

Good catch. You are absolutely correct. Yes, it was "sort of" intentional. And no, there were no potions involved.
       Warren T is a runt cat, smaller than the cats but larger than the adult mice, not by much. The idea was that he was the bully of the cats. A little guy with a huge ego and a bullying attitude, sometimes referred to as a Napolean complex. And, with his small size and a crude disguise, he could pass himself off as a rat and a "friend", offering to help new-comers to America, get a job. Tiger on the other hand was a huge cat, two to three times as big as the cat gang members, and literally towered over Fievel.
        Many times, trying to stage the various character sizes, like Warren T. with Fievel vs, Papa with Fievel, together within their environment meant we took some liberties or artistic license to avoid cutting off parts of their image on screen and give the shot a believable and pleasant appearance, without having to draw tiny minute images of Fievel.
        Actually, as far back as I can remember, we've never had a viewer write to us about the discrepancy in the Warren T's size. We thought that some in the audience might have brought up the size changes on Tiger during the "A Duo" song performance. Which, was a much more radical discrepancy. But, no one did.
       Again, good catch and thank you for asking about it.

I just talked to one of An American Tail's animators on the phone, and he said the size change to Warren T. was intentionally made depending on the scene he was in. But the movie still doesn't bother providing an in-universe explanation for this. It feels like a plot hole. Maybe he really does have growth and shrink potions, and we just don't see him use them.

Does Warren T. have potions that make him grow and shrink?

I noticed that in The Great Longneck Migration, the characters keep on referring to dreams as "sleep stories." But in The Secret of Saurus Rock, Littlefoot literally says that he had a bad dream. A little consistency is all I ask! Do the writers always have to come up with cute-sounding alternatives for words we take for granted?

Oh right.. That's understandable....

Then again, he probably also hated An American Tail: Fievel Goes West, which I thought was great.

Why exactly do people like the sequels, aside from nostalgia? Wasn't the first movie supposed to be self-contained?

Have any of you seen Marzgurl's reviews of the Land Before Time sequels? They aren't up right now because Blip was recently shut down, but they will be back eventually somehow.