Peeling away some of the flavour of your question, I think it boils down to: "are there non-lexical, non-pronunciation cues that distinguish US English from Canadian English from British English from Australian English?"
Assumptions
I don't think your question can be answered without making a number of assumptions. I'll list the ones I've made below.
"Non-pronunciation cues" would be those that don't come out in the way words are pronounced. "Non-lexical" would mean that you're strictly not looking for differences in word choice, including spelling variants. However, the line between syntactic differences and differences in word choice is very blurred — for example, the difference between "Scotland Yard are" (UK) and "Scotland Yard is" (other varieties) is technically a difference in the choice of a single word. However, I include this as a syntactic difference since it pertains to number agreement. I also exclude things like "learnt/dreamt/spelt" vs "learned/dreamed/spelled", which under this definition are just choices in the surface form of the word (where the underlying role is the same)
I think you are probably aware also that each of those English varieties is not a homogenous, uniform variety, but instead a multitude of lects which each have differences. So I'm going to assume that you mean "Standard X" for each of those varieties of English. This naturally requires the asker to assume what "standard" means for each variety, but I will venture that you mean a relatively non-marked variety which might reasonably be heard on broadcast TV or in printed media such as newspapers. This would rule out certain regionalisms such as US Midwest "needs washed".
Also note that many (but not all) of the below are basically tendencies rather than 100% precise diagnostics. This is because the various Englishes have to varying extents influenced each other, importing and exporting constructions back and forth. The most reliable diagnostics are those that distinguish British English from the others.
Under the above assumptions, here are a few diagnostics. Please note that I'm personally only aware of one syntactic diagnostic that distinguishes Standard US from Canadian English (and it's really a lexical difference so it probably fails my own criteria).
General US English
- "had gotten" (US, Canadian) vs. "had got" (other varieties)
- "I'll write you" (US) vs "I'll write to you" (other varieties)
- "go X" and "go and X" both acceptable (e.g. "go take a bath")
- "come with", "go with" without a phrasal complement (e.g. "Are you coming with?")
General Canadian English
- "As well, ..." as a sentence-initial conjunction while other varieties disallow it and instead have "In addition, ...".
General Australian English
- "in hospital", "at university" and not "in the hospital", "at the university" (US)
- In spelling out numerals, "one hundred and thirty four" and never "one hundred thirty four" (US)
- "Three pounds thirty" and not "Three pound thirty" (UK)
- “do” as pro-form not generally allowed after a modal (in common with English varieties apart from UK)
General British English
- "He was sat on the wall" (UK) vs "He was sitting on the wall" (other varieties)
- "He was stood in the corner" (UK) vs "He was standing in the corner" (other varieties)
- "in future" (UK) vs "in the future" (US), in the sense of "from this point onwards"
- "in hospital", "at university" as in Australian English
- In spelling out numerals, "one hundred and thirty four" and never "one hundred thirty four" (US)
- Treating morphological singulars as grammatically plural: "Scotland Yard have not received any complaints..." (UK) vs. "Congress has not agreed..." (other varieties)
- When referring to pounds and pence, British English accepts "three pound thirty" while other varieties would expect "three pounds thirty". I believe this is specific to the lexical item “pound”, since UK English does not allow e.g. *Three dollar thirty.
- "go X" dispreferred in favour of "go and X" (e.g. "go and take a bath")
- Curiously, “should” in the complement of verbs that might take the subjunctive is more common in British English:
- “I request that he should be transferred to another department.” (UK) vs “I request that he be transferred…” or “that he is transferred…” (other varieties)
- British English allows "do" as a pro-form after a modal while other Englishes do not:
- "Will you do it for me?"
"I will do." (UK) vs. "I will." (other varieties)
- "Do you have two pound fifty?"
"I should do.", “I might do.” (UK) vs "I should.", “I might.” (other varieties)
- "Did he like it?"
"He must have done." (UK) vs "He must have." (other varieties)