It seems that the main criticism of Batavia is about its theme - the game mechanics is great, but it is hard to understand what it represents theme-wise.
I haven't played Batavia (yet), but based on wonderful reviews (thank you, EndersGame), I'll make an attempt to patch up the theme.
There are many different type of actors in the far east trading.
Producers: represented by the warehouses on the board.
Merchants that by from producers: represented by the players.
Harbor masters, local kings, and other middle-men between merchants and
ships: represented by the auction and the take-two-cards option.
Company officials: represented by the company seal.
European kings/queens: interacting with the canon.
In order to close deals with East India companies, merchants must gather information (ship cards) from harbor masters and local kings. Gathering information is the same as paying money (promissory notes). The money the local authorities gain is soon spent on small purchases of items or good-will among other merchants in the region.
Picking up cards:
A player who has very little information about the East India companies can gather more (picking upp two ship cards) by slower means than the big buy at "the auction". It is hard work, and the player cannot do anything else meanwhile.
Playing ship cards:
Once you have enough information about the needs of an East India company, you can try to become its main supplier. You negotiate directly with the company officials (play ship cards), and if a company considers you the best suited supplier, you get exclusive rights (the company seal). However, a person who tries to appear important, but is not, is soon neglected by everbody else. Therefore, you cannot make an attempt for exclusive rights unless you actually gain them (or alreade have them) with at least one company. If you gain (or already have) at least one company seal, you are considered generally important, and your efforts (played ship cards) with other companies are not wasted.
There's a fine line betwen competition for exclusive rights and petty corruption. When the canon reaches its threshold, one European king/queen (the most suffering one, according to the ship cubes) will decide to do something about all the leaks in the system, and replaces all company officials with new people. Old information and old relations are suddenly meaningless, and merchants compete anew for the exclusive rights with the new administration.
Moving the merchant to a trading post:
With your exclusive rights, you can be at the right harbour with the right goods to close a nice deal.
Placing a crate in a warehouse:
As you close a deal with an East India company, you by large amount of certain goods from the producers. This gives you a position as a valuable customer among those producers.
Scoring for warehouses:
The merchant who at the end of a season is considered the most valuable customer (has most crates in the warehouse) gets a very lucrative deal with the producer, for future seasons (adds to the score). I ncase of a tie, the producer will split the deal among all winning merchants.
Scoring for trading posts during play:
Though your main buisiness idea is to pass goods from producers to companies, you can sometimes use your position to close special deals between the companies directly - for example administer an exchange of excess silk from the Danes for excess tea from the French. The more compaines involved, the more money you get, but timing is everything - these kind of deals cannot be delayed.
So - that's it. I do not know how much different from the rule book this theme is, but it makes sense to me, and it may help my own imagination when I play (and I will).