There may well have been remains in the roads still, I wonder if there are any there now? I'll have a look at some point.
As far as fun and girls go, you were probably lucky to get away in one piece and not wake up in the hold of a ship heading for the Baltic with lipstick stains on your collar...
Sadly, there aren't any remains any more.
I lived in Teignmouth all the way through my childhood (early 80's) and remember walking into town and looking down at the railway, from the gap where the Old Quay Signal Box used to be. I can not recall whether the Signal Box was still there at this point, or whether it had been demolished.
The area of the Old Quay, abattoir and trawler dock was redeveloped and modernised in the mid 80's, including a minor bit of the road structure above Alexandra Palace, all of which are still in place today.
The former Quay and docks between the beach at Shaldon Bridge and Polly Steps were redeveloped to include a massive grain warehouse, which I remember playing in on sunny Sundays, and a new weighbridge.
There is nothing particular of note in the way of old relics from Shaldon Bridge all the way through the railway line and out the other side of the station anymore, including the Quay. Most of the diamond weight restriction signs on the many little road bridges over the railway were all removed at a similar time.
If there are any track remains left, then it's possible that they are buried under the concrete; but otherwise nothing really obvious in the way of history.