The handguns used by the Secret Service agents and uniformed officers during the whitehouse attack are SIG-Sauer P228 pistols. In real life, the 9x19mm P228 was used by Secret Service until it was replaced by the SIG-Sauer P229 chambered in .357 SIG.
The Heckler & Koch MP5A5 can be seen being used by Secret Service ERT members in the White House attack, fitted with Surefire dedicated forend weaponlights.
The Commandos who raid the school are all armed with Dart Guns in addition to their P90s to coincide with the President's concern of "A dead mutant kid on the 6 o'clock news".
The FN P90 can be seen being used by Col. Stryker (Brian Cox)'s Black ops team on their raid on the Xavier school. They are fitted with tactical flashlights and suppresors, though the suppresors don't seem to work as the weapons aren't suppressed at all when firing.
Grenades are used by the commandos at the school as spike grenades and by the soldiers at Alkali Lake though they are likely the same prop.
Spike Grenade
The Commandos that raid the school all seem to have some kind of spike grenade though it is likely a fictitious weapon meant to be planted on walls or ice.
Magneto (Ian McKellen) uses his magnetic powers to pull the pins on the Alkali Lake soldier's grenades to kill them all. Although portrayed as High-Explosive Fragmentation (HE-Frag), they look more like the M84 stun grenade than any HE-Frag grenades in the inventory.
Boston Police Department officers can be seen using Glock 17s as their sidearms in the film, one of them shooting Wolverine (Hugh Jackman) in the head, though he survives the seemingly fatal shot and is able to walk away, much to the officer's bewilderment.
Later on the film Sgt. Lyman uses a Glock 17 on Mystique but when he is guarding Cerebro 2 it changes to a Walther P99.
Col. Stryker's soldiers at the Alkali Lake complex can be seen armed primarily with M4A1 carbines fitted with RIS foregrips, tactical flashlights, and laser pointers.
Wolverine was given special dogtags before his bones were laced with Adamantium, interestingly however his dogtags are the Canadian type, not the American, which would be correct for the comics since the Weapon X project that created Wolverine was the Canadian government.