I would say that the primary difference between spoken and written English would be the manner in which practicing both has to be done. For spoken English, I think that being able to practice in groups and within constant social interaction is of vital importance. I am not sure that spoken English can be fully grasped in isolation and without some level of social interaction with others. It is in this realm where one's spoken English improves and develops fluency. Writing English is another realm where practice is needed. Yet, this particular aspect can be done in a bit more isolation. While feedback is needed, this can be done through technological means and in forums where the focus is on the individual and the writing. There does not have to be such a socially interactive component present to the improvement of written English.
I think there are several differences between written and spoken English. To categorize it, I suppose it could be said that written English is more formal (usually) and spoken English allows for accent and dialect differences.
Here is an example of an acceptable spoken sentence:
The musician didn't want their song to be released until the end of June in order to boost sales just before the big tour.
However - in writing this would be wrong. The correct way to write it is: The musician didn't want his (or her) song released until...
Note: One singular musician cannot be represented by the plural possessive pronoun "their" - but MLA has said this is acceptable when speaking. We do it all the time because using "his or her" verbally is muddy - also when speaking we often want to keep a person's identity hidden so we use "their" instead of revealing whether we're talking about a male or female.
Other accent/dialect examples:
Y'all in the south = you guys in the north. Waiters and waitresses swear though, that referring to a table of both men and women as "you guys" often results in a lower tip. On the other hand, not many people say, you all. Again - slow, awkward, muddy. And certainly it isn't proper English to write y'all. In fact, my southern friends do it on Facebook all the time and spell it wrong: ya'll - making it worse: "ya all." Aweful.
I think the main difference is the amount of freedom that people are granted when speaking as compared to what they are granted when writing.
People write in all kinds of different styles, but there is a more accepted main-stream type of writing that is generally found in most newspapers or magazines and it mimics in some ways the English spoken on the news or other shows like them.
But spoken English is allowed an enormous amount of freedom as even main-stream political speeches can be filled with various modifications that we would likely not accept in written form. People can drop their g's or speak in an accent or use absurd expressions that would simply look ridiculous in a written piece.
I would say that the main difference between spoken and written English is that - linguistically speaking - in spoken English a sentence is often just an ellipsis (=the sentence is syntactically not complete). Moreover, sentences in spoken English are generally much shorter than in written English. Less subordinate clauses are used in spoken English. Concerning diction, in spoken English dialectal and colloquial words are used that wouldn't be used in written form.
It is very interesting to listen carefully to a dialogue. It is amazing how people understand each other, though so many syntactical units are left out.