Do airline pilots routinely carry out "gross error" checks?
I agree, Malaysian MH132 was a Non-Event.   If the pilots had any concerns over the slight variation in their routing, they should have mentioned it before they loaded it into the Flight Management System (FMS).

I currently fly long haul B777 for a major airline. I can't speak for others, but at the airline I work for we do many "gross error checks". Some are done in flight planning, some during the loading of the FMC, and some are done during the flight.

While still in the flight planing area, the Captain and First Officer will look at the total routing in regards to wind, temperature, turbulence, volcanic activity, etc.  Often a call is made to the dispatcher who generated the Operational Flight Plan (OFP) to discuss the routing, expected levels of turbulence, and fuel reserves.  About 20% of the time the Captain will request a slight change to the routing or additional fuel be added.  A new OFP is then generated and it will be designated "Release 2".

Both the flight plan route and ICAO flight plan route are printed on the OFP and we compare the two.  I have never found an error in the 17 years I have been doing it, but we still do it every time. 

Once the Captain, FO and augment pilots ALL agree, the OFP is officially accepted and we head to the aircraft. (up to 4 pilots on Ultra Long Haul flights)

When we get to the aircraft we run though the basic preflight checks, and then the flight plan is downloaded to the FMS using the Aircraft Communications Addressing and Reporting System (ACARS) digital datalink system. The departure runway and SID is also loaded at this time.  

Before we "activate" and "execute" the routing, the Pilot Monitoring (PM) reads the entire FMC routing and the Pilot Flying (PF) compares it to the OFP.  

After runway takeoff performance data is loaded we then check the "Legs" page of the FMC for a logical sequence of legs. We generally just check to make sure there are no course reversals on the various legs of the route.  If there are any user defined waypoints (Lat/Long waypoints) we perform bearing and distance checks of  the FMC against the OFP. This is done with the the Heading Reference switched to TRUE heading instead of Magnetic for more accurate numbers.  These bearing and distance checks are not done for "Named" waypoints, only Lat/Long waypoints. 

Wind data is then requested and then loaded via ACARS.

Next is a check of the FMC distance compared to both the OFP distance and Great Circle Route distance.  The FMC distance is almost always somewhere between the OFP distance and GCR distance. This check is one sure way to spot a routing entry error.

Finally a check of the FMC and OFP predicted fuel over destination is done. If there is a large difference, it means either the routing or winds were incorrectly entered. 

Once airborne there are more checks:

In the old days before GPS we would check the accuracy of the Inertial Navigation System (INS) as we approached the coast for any over water flight. This was usually done using a VOR/DME fix. 

Once airborne we again check bearing and distance as we approach each user defined waypoint (Lat/Long waypoint). Once past the waypoint by about 5 mins we then plot our current Lat/Long on a plotting chart to insure we are still on course.