Not very; less than American and British English, probably less than Northern and Southern American English. You can read and write for a long time without knowing or showing which dialect you are in.
The least substantive issue is whether to use a comma with 'la. And, if you decide to use one, whether to put it before or after the 'la'. Commas also play a role in more substantive issues, but even here they are usually still considered optional (though occasionally appreciated). The most common place for them is before the terminal prepositional phrases, after the DO, where they prevent the preposition from being asorbed as a modifier in the DO: 'ona li pana e tomo tawa mi' (“He gave my car”) vs 'ona li pana e tomo, tawa mi' (“He gave me a house”). Other possible places are in modifier strings, to prevent new modifiers being caught up in earlier 'pi' phrases, and in 'la' strings, to separate out left grouping ones from the usual right groupings. The PP commas are actually a rule in one dialect (Lope's), the others are just occasional uses for some people.
The most substantive differences are in vocabulary. There are about 118 words that all dialects accept and understand essentially the same way. Then there are about half a dozen words which some dialects have but other lack or treat as mere variants of other words. The not firmly fixed words are 'esun' “shop”, 'kin' [emphasis], 'kipisi' “cut”, 'monsuta' “fearsome” 'namako' “excess”, and 'oko' “eye”. A few people have occasionally also revived an old word for a particular purpose.
In addition, there are a number of variations on how generally accepted words are used: some allow only 'wan' and 'tu' as numbers; some allow 'luka' (5) as well, some even allow 'mute' (20) and 'ale' (100). Some people use 'lukin' for “look for, seek”, others prefer 'alasa'. Some take 'kute' to mean “obey”; others don't. And there are probably others of this sort.
There are even a few variations in grammar. As noted (FAQ 3), some people still take 'kepeken' to be a verb (with 'e' before the DO) when in the verb position. Others take it as a preposition everywhere. Despite very different descriptions of how 'pi' works (FAQ 5), most people deal with actual cases about the same way. The most common difference is over whether prepositional phrases as modifiers need 'pi'.
Since there is no readily available good source of idioms (compound words) , some people will know some that others do not, with inevitable loss of communication for the moment. In a few cases – those around 'toki' being the most common (FAQ 4) – alternate idioms are fairly common.
But, for the most part, people know of the variations (or simply don't notice them) and get on with the substance of what is being said.