Jerry Mitovica's talk is good, apart from the fact that he keeps wandering away from the mike.
Drivers of sea level, and thus potentially sea level change, in rough order of scale, and particularly as observed relative to the coastlines:
Gravitational attraction to the mass of the continents raises sea levels near continents by large amounts - potentially 100's of meters. So this elevation difference varies depending on distance from the continent and the size of the continent.
Ice masses on the continents contribute further gravitational elevation near continents. Loss of this ice causes large scale sea level falls near those continents. Loss of the Greenland ice sheet would lower sea level at the Greenland coast by around 100 meters. This means that each separate region of ice loss has a specific 'fingerprint' wrt how much it effects sea level at different points on the Earth.
The distribution of densities inside the Earth's Mantle - it isn't equal density. Generally sea levels follows the lines of equal gravitational strength - the Geoid - not a single even height. Measured from satellites, sea levels are more bowl shaped, higher near the land, lower in the center of the oceans, but also perturbed by mass distributions inside the Earth.
Land Ice Sheets melting due to the glacial cycle
Isostatic Adjustment as the sea floor sinks due to the extra weight of water in the ocean after the glacial melt. The ocean gets deeper under this extra weight so relative to the coast, sea level falls
Isostatic Adjustment of those continents previously supporting ice sheets that have melted the ice retreated causing those affected continents to rise.
Areas of subduction/mountain building that can result in localized uplift or subsidence
The West Antarctic Ice Sheet is a special case. It is a frozen sea with a large weight of ice sitting on top of it. So if it melts, the 'sea floor' of the West Antarctic 'sea' will rise where as the rest of the oceans sea floor sinks.
Groundwater/Oil/Gas extraction that can result in localized subsidence of the land. Particularly an issue near major cities that rely on groundwater.
Redistribution of water in the oceans as ice melts, with more of the melt water moving towards the equator causing extra elevation there due to bulging at the equator caused by the the Earths rotation.
Seasonal or occasional patterns that change the amounts of rain falling on land. With a lot of rain, storage on land of water increases - dams, lakes, but particularly ground water. Two effects; less water in the ocean, and a small increase in the gravitational attraction the continents exert due to the extra mass of the water. Dry periods have the opposite effect.
Similarly the normal seasonal fall of rain and snow fall and melt affects global sea levels - Northern hemisphere has more land so in it's winter sea levels are lower than during the NH summer because there is more snow and water on land. Also the change in gravitational effects due to the uneven distribution of this results in uneven distribution of sea level changes over the seasons.
Ocean currents producing localized elevation. Circular currents tend to elevate water levels at their center. Longitudinal Currents can also push water ahead of them producing elevation. The Gulf Stream for example elevates water levels along the US East coast.
Winds producing elevation differences due to pushing water. Storm surges are dramatic short term changes, but prevailing winds such as the trade winds have a more consistent effect.
Differences in water temperature and salinity causing differences in density. Less dense water will have a slightly lower gravitational attraction to other water around it. Also, when water has a lower density this can partly change the pressure profile below it. As a result regions with less dense water in the water column will tend to sit a little higher.
Changes in air pressure above the ocean change water level below - water tends to flow away from under high pressure system.
The monthly lunar cycle as the moon is nearer / farther from the Earth.
The normal tides.
Maybe there is something I have missed.