Well, the May Constitution attempts to avert the affects of serfdom without actually abolishing serfdom; this is going to cause conflict down the road. If comparing to the US serfdom for Poland could be what slavery is for America ITTL. I don't think things will come to ahead too soon as the nobles are the ones instituting this Constitution, but if Poland isn't Partitioned then I see no reason why she wouldn't survive past the Napoleonic period and until the 1848 revolutions; at which point she'll have to abolish serfdom like OTL Austria, or purge the revolutionaries and face a larger one later like OTL Russia.
I'm not sure about the shared power of the executive. It seems to be some sort of merge between the Swiss model and British model; i.e. acts of the King required the countersignature of the respective minister, and like the British the respective minister is responsible for the King's actions (e.g. the King can do no wrong), however the King does take an active role in government and can vote in the (Straż Praw) executive council. This seems like it would either work unexpectedly or fail splendidly.
Also the Constitution stipulates (in the Constitutional text!) then when current King Stanisław August Poniatowski dies the throne would pass to Frederick Augustus I, Elector of Saxony and the House of Wettin would de jure be the royal house of Poland. I'm just wondering how 'Polish' Frederick Augustus would be while King of Poland concurrently with Elector (and later) King of Saxony. Looking at Frederick Augustus' life IOTL it seems like even when he was the Duke of Warsaw he was far more concerned with his Saxon holdings than his Polish ones. So ITTL this could go several ways. Off the top of my head either Frederick Augustus is 'King' of Poland but in actuality the Sejm runs the country and everything works out as best as can be expected, with the Marshal of the Sejm largely taking over the King's role in a British sense (the Marshal being unable to vote in the Straż Praw), or the Polish people and eventually the Sejm tire of their 'King' turning his back on them and conflict ensues; which in and of itself could go several ways as well.
Another potential problem I see that the Constitutional text strictly outlaws confederations and confederated Sejms; I'm not sure about the intent of the language of the bill, but if I'm reading it correctly it would appear to outlaw political parties; this could be a huge issue.
One of the largest problems within the Constitution is that the text itself limits amendments to being made once every twenty-five years. The text itself states;
"Preventing on one hand abrupt and frequent changes of the national constitution, and on the other recognizing the need to perfect it after experiencing its effects upon the public weal, we fix a season and time for revision and amendment of the Constitution every twenty-five years. We desire that such a constitutional sejm be extraordinary in accordance with the provisions of a separate law."
This to me seems to imply that the Constitution is only 'open' to amendments at 25-yr periods, in which a special committee will debate changes to the body of the text. This is going to severely curtail efforts in a variety of fields. Imagine if the 14th and 15th amendment to the US couldn't be even debated until 1890 because the timing of the 13th. Also, expect some hi-jinks on the behalf of the elites/conservatives during this amendment period to only allow the smallest amount of and least radical amendments to be discussed. That serfdom issue is starting to look a lot worse now.
But really the big issue is that the May Constitution is to the US what the Articles of Confederation were, and then plus some.In addition to the Constitution there's also the Free Royal Cities Act (April 18, 1791), the Declaration of the Assembled Estates (May 5, 1791) and the Reciprocal Guarantee of Two Nations (October 22, 1791) which are all considered 'Constitutional' texts during Poland's reform process. The Constitution itself was reformed, fleshed and in general tinkered with in a number of ways between May and June of 1791 by the Sejmiks (regional parliaments), regional courts, the Straż Praw, the national police commission (a 'Justice' Ministry of the Straż Praw), and the municipal administration of Warsaw. Even one of the primary authors, Hugo Kołłątaj, admitted it was a work-in-progress, even stating that work was underway on "an economic constitution... guaranteeing all rights of property [and] securing protection and honor to all manner of labor." He also stated that a 'moral constitution' was also being debated, along the lines of the American Bill of Rights and the French Declaration of the Rights of Man and Citizen.