The policy flying out of Santo Domingo is different than that flying out of Miami, and Miami also changed policy daily for a while.
Out of Miami, you can carry lighters. Out of Santo Domingo, no lighters, no matches, and it doesn' t matter to them if they light or not (no gas). I collect them and they took the one I was carrying on my person so now I carry one that doesn't look like a lighter and mount it to my keychain.
They do not sell lighters anymore once past immigration when leaving Santo Domingo.
Batteries? That's a new one. For a while, they did not allow alkaline batteries out of Heathrow, but that was pre-911.
In Santo Domingo, they typically have a basket filled with all the nail clippers, razor blades, scissors, anything that looks like it could be used as a weapon which means anything with a point, ... You are told this AFTER you have already checked your luggage. The entire airport once past Customs is now all non-smoking as well but they still have ash trays. They sell electronic appliances past customs, and all those items use batteries (mostly rechargeable). I don't recall if they sell alkaline batteries o nicad's that look like alkalines (as in AAA, AA, C, D sizes). Every laptop has a battery, I doubt the would take one of those (US$100-150 to replace). Watches also have batteries, as do pagers, pen lights, cordless mice, ...
I would have complained and made a scene, but it was probably policy that day. I know the lighter thing came about from the guy that tried to ignite some plastic explosives hidden in the sole of his shoe with matches and for a short time, was also disallowed in Miami.
I always ask now at the counter what I can and can't carry and if they give me crap at security, I'll call they airline rep that told me different and make them retrieve my checked bag. Else I won't get on the flight and they will have to remove my bag anyway. I fell asleep once during boarding and woke up just before they shut the door. Security then proceeded to practically strip me. I guess I was being too slow to put my shoes back on and the gate agent threatened to lshut the door, leaving without me. I reminded them of the policy of not flying with passenger baggage without the passenger on international flights, and pointed out that they had already picked the "random" searches, that I had cleared security, and that I was doing the best I could. This was in Miami.