Like so many other characters in crime stories, Grayson made what could have been a dangerous mistake when he didn't wash his hands after handling the poisoned glass in von Stolb's quarters. He picked it up from the inside to avoid smudging fingerprints, but because the glass contained residue from the deadly poison, the residue would have remained on his hands.
The building at 1693 Market St. in Braun's painting is miles away from his apartment on Clay St. from where he supposedly painted the scene.
It is mentioned more than once that tracing the telephone number would take a long time since the call was placed using a dial phone instead of through an operator. However, a rotary dial makes the same amount of clicks as each number dialed (except it makes 10 clicks when dialing 0) -- and the sound of the dialing is clearly heard on the recording. Simply counting the clicks would give them the number dialed.
Grayson from Scotland Yard would be introduced by a rank e.g. "Inspector" not by "Mr.", in same way as FBI personnel are introduced as "Special Agent".
In his Lakeview hotel room, O'Hara answers the telephone with a very professional "O'Hara speaking". But 30 seconds later, he answers with a simple "Hello".