Assuming that Other People are Mind Readers is commonly described as an aspie trait though I don't think it's the result of aspie assumptions. Instead I think it's an NT interpretation of their behaviour.
Behaviour 1: Sudden changes of topic in mid-conversation
This stems from the aspies difficulty with small-talk. Aspies won't stand around discussing the weather but tend to discuss and resolve a single topic, then quickly move onto the next. NT conversation is quite different and they will tend to move to a neutral topic before starting on something completely different. There is nothing wrong with either approach but NTs talking to aspies often get lost at this point and think that the aspie has found something new to add to the original topic.
Behaviour 2: Expecting People to have a Shared Memory
A lot of things come back to the aspie memory. Aspies often have very clear memories of events and quotations. In conversation, they may drop a remark which links back to a particular memory but even if the NT was present at that event, it could have been years ago, or the particular part of the event to which the Aspie is referring may not form a large part of their memory.
Example: An NT spills a drink at a party. The Aspie might say, "you have a habit of spilling drinks - lucky it wasn't orange juice". This could refer to an event at a picnic more than two years ago where perhaps that NT had knocked a bottle of orange juice over. NTs do not remember events in such detail and would therefore have no idea what the Aspie is talking about.
Similar things happen when the Aspie drops a quotation from a particular movie or song into the conversation without warning and without acknowledging the source. The NT becomes confused.
Behaviour 3: Leaving half the words out
Aspies often get the feeling that they are not being listened to. This is probably something to do with not understanding the visual and tonal cues in conversation. What often happens as a result of this is that the aspie trails off in midsentence.
Similarly, sometimes aspies have a tendency to start a conversation in their head and only verbalise the last parts. This is particularly common when they've just had an idea and pick up where a mental conversation, rather than a real one, left off. For this reason, NT's have a great deal of difficulty following aspie conversation and assume, not wrongly in this case, that we are expecting them to be mind readers.