Overall though, I think the Mongoose version is very close to the original, from my brief readings. There are a few minor tweaks, but it seems to retain versions of all the same subsystems and whatnot. Hopefully they have been tweaked some, because a lot of them were not all that solid to start with. All of them, like the trade system, WORK as story-generators, but if you actually try to, for instance, have a PC build a trading business using the trading rules, you will soon find out that they are unworkable as an actual system. I think various later editions 'fixed' those issues in different ways.
The only other real issue I ever had with Classic Traveler is that the space combat system is not really all that workable. Again, it is not bad as a story generator, but you can't actually play 'space combat' with it. Its more good for describing how your scout ship got into a huge jam when the navy patrol cruiser shot a hole in the maneuver drive...
I've never used the classic Alien Modules. In our current game there are no aliens (as far as we know) other than the mysterious ones the PCs are investigating.There are some nuance level differences with the alien species that I cant really speak to. Some classic fans can be pretty negative about them. I dont think too much of them myself, but find them workable. Alien species are the weak point of Traveller (any edition) for me.
We have used the trade system once - the Merchant Prince version - and it seemed fine. I have no idea how it would work on a longer term basis.
We have had three episodes of space combat. Once the PCs lost their ship. Once they defeated an enemy ship. And once they took a hit which cost them millions of credits to repair. It doesn't support Star Wars-type space combat, that's for sure!
It's a lot of work to build advanced character gen systems for every servcie.the later character gen which goes year-by-year instead of in 4-year blocks was a little more fun and produces better rounded characters
Andy Slack's solution for standard characters (which I know from Best of White Dwarf v1) is to throw one die for each term: on a 1 to 4 get that many additional skills, on a 5 choose a skill, a 6 is a bust. I think the Special Duty line on the chart is a good option: throw to get an extra skill throw, and the way we work it (which I guess I took from MegaTraveller, but maybe I made it up) is that a throw of 4 more than needed is two extra skill throws or choose a skill. This gives well-rounded characters but keeps PC gen reasonably quick. I think it's a good approach.