According to FAA §25.1535 Appendix K,
The airplane flight manual must contain the following information applicable to the ETOPS type design approval:
(b) Required markings or placards.
(e) This statement: “The type-design reliability and performance of this airplane-engine combination has been evaluated under 14 CFR 25.1535 and found suitable for (identify maximum approved diversion time) extended operations (ETOPS) when the configuration, maintenance, and procedures standard contained in (identify the CMP document) are met. The actual maximum approved diversion time for this airplane may be less based on its most limiting system time capability. This finding does not constitute operational approval to conduct ETOPS.”
It does not require any identification marking on the aircraft itself, though as @woakley5 noted above, a number of aircraft do have them identifying the aircraft as ETOPS certified, like below.
I'm not sure about if any indications are there in cockpit (there are no regulatory requirements, till today that is), but won't be surprised if it is available (in some aircraft, at least).
The ETOPS do have some additional checks. According to Appendix G to Part 135,
(This) This ETOPS maintenance program must include the following elements:
(b) ETOPS pre-departure service check. The certificate holder must develop a pre-departure check tailored to their specific operation.
(1) The certificate holder must complete a pre-departure service check immediately before each ETOPS flight.
(2) At a minimum, this check must:
(i) Verify the condition of all ETOPS Significant Systems;
(ii) Verify the overall status of the airplane by reviewing applicable maintenance records; and
(iii) Include an interior and exterior inspection to include a determination of engine and APU oil levels and consumption rates.
I'm not sure how the AA Flight 31 Flight and ground crew missed these checks.