I had this in the Ginger Cat, when I had to talk to Betty's boss. Here I could not talk to her and was stuck at inspect the work place. Using a clue, he then walked to her and started the conversation.

Now I am sitting at the table in the doctors house 'Question the Victims Brother' and cannot talk to him, nor get up or do anything else "It is not the right time".

p.s. using a clue or quit and reload the game, then you can talk to them. It's a bug.
pps. then I observed him and was straight stuck again, reloading and now can talk to him again.
And was stuck at question Thora Gray again...
And I was stuck again when I had to observe everyone...

pps. OK, if you have the menu at the bottom right open, you cannot talk to or observe people but interact with objects. Close the menu and you can continue with the story!

Frequently quitting and reloading will fix errors where the game does "forget" to change a quest status etc.

Could be, but this what I described was caused by the open menu. It is something you may not think about...

Stuck in Poirot's apartment. Will try your suggestions... so far no luck.

Ok on steam forums there's an official answer to these questions. There's a way to use a backup save:

If you are really stuck, you can use a backup save, here is what to do:

- Go to C:\Users\[USERNAME]\AppData\LocalLow\Microids\The ABC Murders\Profils
- Now choose the folder corresponding at your save in game (0 is for the the top save, 1 is for the middle and 2 is for the bottom)
- Open the folder with the highest number
- Copy all the files Inside
- Come back in the previous folder
- Paste and replace all the files here.

If everything went good, you should now have a previous save as main save.
Start your game and give it a try!

Please note that we're currently working on this, it'll be fixed so you won't have to do this forever.
Sorry for the troubles.