I don't get the complaints about this. He wasn't falling in love. He just doesn't like to see a woman scared / in pain. This is true in all the movies. It's the same reaction when he explains to Melina in FYEO about revenge and when he comforts Vesper in the shower in CR.
I was okay with this, too. It reminded me of how Fleming wrote that Bond was a sucker for "a bird with a wing down," and in that sense it seemed in character. He "wipes" the tear from Elektra's cheek on the video screen as a reflexive move; Bond is driven to protect and "rescue" women in peril, but ultimately that's about as close to "relating" as he ever seems to get. Certainly he's incapable of a long-term relationship. Even Tracy just boils down to the most-in-need-of-rescue of the lot: she even needed saving from herself!
That said, TWINE as a whole was a train wreck, and near the bottom of my list.
Getting back to the topic, I thought Brosnan was stiff and awkward for much of GE, always posturing and trying overly hard to look tough and cool (but in the end just looking like a runway model who's been told to pout instead of smile). There were a couple great little moments, like when he's obviously delighted at his impromptu, frivolous and highly dangerous car race with Xenia and again when he's calmly fiddling with a bomb while bullets buzz by his head in 006's base, but overall I was disappointed he brought almost none of the charisma and screen presence he'd shown in his TV career. In trying so hard to be taken seriously as an action hero, I thought he threw out all the things that had made him appealing in the first place.
With TND, I thought he looked a lot more comfortable, and a bit more physically solid to boot, so I accepted him more easily as 007. It probably helped that they were too busy piling stunt scene on top of stunt scene to stop for the usual dime-store psychology crap.
Nobody could have made TWINE work, and Brosnan surely didn't, but on the up side it may have been the best he looked in his tenure.
DAD was awful ultimately, but for the first reel, Brosnan does a very good job, especially in the Korean prison sequence, where he's had the crutches of Brioni suits, hundred-dollar haircuts and flashy gadgets all taken from him but has to figure out how to keep Bond "Bond" even in ratty clothes and a scraggly beard. Especially good is the scene where he's about to be executed and seems to finally accept he's reached the end of the line. Soon enough, though. it's back to business as usual, and it's hard to judge a performance when the script is no more demanding than the average Popeye cartoon. I could fault him for having, without exception, the worst one-liners in franchise history, but in fairness what could he do? Chuck the script and write his own lines? That wasn't really his job.
I think Brosnan did what he could with what he was given. For me, his strength ultimately proved his weakness: he was a "shoe-in," such an inoffensive, middle-of-the-road amalgam of all that went before that there was never any serious question whether the public would "accept" him (in contrast with Craig, later on), but then when all his films also turned out to be inoffensive, middle-of-the-road amalgams of all that had gone before, things got very tiresome very fast. Brosnan, for me, is the one Bond actor you could replace with just about any leading man of the era and have his films remain essentially unchanged. He's just sort of "there."