Continuity mistake: When the car cuts the large hole in the ice Bond doesn't move when he finishes the cutting the circle, but we see the view from his car, and he's several feet away. Also the size of the circle he cut out dramatically changes to being a lot smaller.
Continuity mistake: When Bond stops the timer on the bomb in the transport plane, the digital readout shows 3 seconds to detonation. When he restarts the timer to explode the bomb on the bridge below, the time to detonation has rather conveniently changed to 9 seconds. This gives the bomb time to land on the deck before it explodes.
Continuity mistake: When Bond and Milova escape Bratislava it is snowy and wintry. When they arrive in Vienna, which is only 50 miles away and at the same latitude, it is late summer or early autumn, with signs of leaves changing.
Continuity mistake: When Bond exits the tunnel in the Aston Martin they get fired upon by an armoured car - look at the scenery outside the Aston, from inside there is no left turn, but one appears out of nowhere for Bond to take and head down to the frozen lake.
Continuity mistake: When Bond and Necros are fighting on the opium packages behind the plane, in the wide shot we see that Bond is all the way at the top of the bundle of packages - he takes his knife and cuts the net near his knee. In the next wide shot we see that Bond's head is above the top of the bundle of packages, but in the next close-up, packages are dropping from above Bond's head.
Continuity mistake: Midway through their escape to Austria, when Bond and Kara start running from the wrecked Aston Martin, the right-side wing mirror is hanging almost vertical. A few seconds later, when the pursuing skiers arrive, it's only slightly crooked. (00:49:10)
Continuity mistake: When Bond lasers through the police car, the laser is at right angles. But, in close up shots, the angle is different.
Continuity mistake: When Q is demonstrating the stun gas/explosive key ring, when Q holds the keyring it's very slim. However, when it is placed on the desk and emits the stun gas, in close up it is very thick. This is obviously to make such a slim device emit the gas (probably an under the table gag).