Do airliners have any cockpit indication of open doors?
The Airbus A320 has an ECAM (Electronic Centralized Aircraft Monitor) Door Page:

(A320 FCOM - Doors - Controls and Indicators)
When a door is opened, this will also trigger a caution. According to the FCOM, a MASTER CAUT is triggered together with a SINGLE CHIME. The lower ECAM page will also automatically switch to the Door page.
Other aircraft may have similar pages or individual warning lights, like e.g. the Boeing 737 on the overhead panel:

(Boeing 737 NG FCOMv2 - 1.30.15 - Airplane General, Doors - Controls and Indicators)

I can only speculate why the pilots did not recognize the open door earlier in the incident you linked. My best guess would be that they were preoccupied with the engine failure that had just occurred, which will obviously create a lot of other warnings. It is easy to miss the door warning in all of those.