It will be interesting to see the 'decision tree' that the crew used to continue. Upon hearing and/or feeling the event and seeing the #2 paramters (EGT, N1, Oil Pressure, etc.) nose dive, no doubt they cut the fuel supply via switches or fire handle. An apparent assesment of the situation revealed no anomolous conditions (hydraulic fluid or pressure loss, cabin still climbing at normal rate, airplane still behaving normally, no fire warning, etc.). The long term would include, I would think, the potential loss of either #1 or #3 (for unrelated reasons) over pretty much nothing but jungle between Manaus and Bogota - not to mention the fact of a high altitude landing attempt at BOG. Go around could get tricky...
I wonder if the decision included a thrust increase on #1 and #3 or just a slower climb rate. It would depend, of course, on the weight and balance, but I wonder if they bumped 'em a little or to the firewall. I understand that case in point procedures differ between operators.
This 'bump' would be the issue raised above about the age thing. Even older engines just out of overhaul will respond differently from those that are factory fresh. Overboost - even for a short while - could spell trouble. If memory serves, the BA 744 crew that lost one on takeoff out of LAX a couple of years back, leveled at FL03 for about 20 minutes, THEN made the decision to continue knowing, in part, that there are lots of good diversion points prior to going over the pond if necessary.
I understand that the US NTSB is weighing in on this one given the 'N' status of the airplane and its Miami - based operator. So, hopefully there will be good info from this one....