A lot of places around the world have rulers that are fixed to the ground and have been regularly read for many decades.
The process is basically that one person reads the level at regular intervals for several minutes throughout the day (every 5 seconds for 4 minutes, once every hour for 8 hours, starting 4 hours before high tide in my case, not sure if it's exactly the same everywhere). The place is sheltered from waves.
Since tide effects are very well known and there are a lot of such stations, it is actually easy to get an accurate image of the global sea level from all these measurements.
Nowadays, they are also complemented by GPS-based measurements, and the stations themselves are also GPS-monitored in order to prevent long-term ground movement from adding bias to measurements.
Since the measurements are done on a global scale (in my case, I performed those while I was stationed on Kerguelen island) and since they have been done for so long in always the same way, they do allow to compare current results to any previous results with much better precision than 2mm.
Afaik many things affect local measurements, like storms and tides.
For example, if you measure at three points in the US, and one point in Japan, how are the measurements weighted?
Suppose a storm is blowing in the US, increasing the measurements by 1m. How is it being accounted for?
That's why you don't measure "three points in the US and one point in Japan". You measure thousands of points all around the world, so if storms affect two or three of them for a day, the global result isn't significantly affected. For instance, just the French observation network is made up of 90 stations that cover enough of the globe to be enough on their own for measuring a 2 mm rise over two months (near real-time data available on ftp://ftp.sonel.org/tidegauge/rmsl/Demerliac/RAW/).
It's really not as complicated as you think it is, the basic science behind global sea level measurements was established in the 18th century.