The one that always got me was Eisen saying he was communications officer on Victory's maiden voyage. Assuming the Yorktown-class came before the Concordia-class first seen in Action Stations, and that he's fifty (give or take) during WC3, he would've had to have been...what, eight years old at the time? Probably a bit young for the service, but desperate times and all that....
Now, now, you know what they say about people who assume...
... they're technically correct!

We can, indeed, prove that the Yorktown-class is older than the Concordia-class. Action Stations tells us that the lead ship of the Concordia class was fairly new, built as a result of government appropriations in 2629 (and given the time it takes to construct a carrier in Fleet Action, that likely means it's brand new in 2634.) The Heart of the Tiger novelization says that the Victory's class was "designed nearly half a century before the beginning of the Kilrathi War," dating the Yorktown to the mid-2580s. The problem is that tells us only that the /design/ is older, not the Victory herself. After all, Eisen wasn't the communications officer on the TCS Yorktown... the Victory was presumably constructed much later (perhaps, for instance, when there was a desperate need for quickly-produced capital ships in the early days of the war!)
I believe a careful read of Eisen's history can narrow that down. And thinking this through, I believe I have a new theory. First of all, you are right if aiming at the low end of the scale: the character description in the Wing Commander III script does claim that he is "IN HIS FIFTIES." And while it's never an absolute indicator, Jason Bernard was 56 when he appeared in the game. Wing Commander III is set in 2669, which would suggest his birthday being somewhere between 2610 (59) and 2619 (50.)
Wing Commander IV (four years later, 2673) then claims that "I fought with Captain Dominguez [of the Intrepid] 40 years ago during the Venice Offensive." That would seem to put whatever the Venice Offensive (a confused WC1 reference, a retroactive battle of the Pilgrim War?) is in 2633 and suggests that he's on the older side of the scale. If he was at least 18 years old when he served in whatever this battle was then he would have been born between 2610 and 2615, making him between 54 and 59 in Wing Commander III.
The Wing Commander IV novelization throws a bit of a wrench into this. It reads: "[Captain Dominguez] was two classes ahead of me at the Academy. We served together during the Venice Offensive. That was three decades ago." In the past we've taken this as a bit of a retcon (swapping the 30 and the 40)... but instead I'm going to argue now that the 'three decades ago' refers to when he was at the Academy (two classes behind Raoul Dominguez) and not a contradiction in when the Venice Offensive took place.
Which seems a little bit strange at first, but actually makes a whole lot of sense. Recall his reference in Wing Commander III: he wasn't shaving when he first took the helm. If he'd attended the Academy out of high school and gone through the four-to-five year program then he'd certainly have been shaving by the time he graduated and started serving on warships... but if he enlisted to fight the Pilgrims or the Kilrathi, he could have been on the front lines as a teenager.
The rest of the story writes itself: on or around 2943 he attends the Academy and becomes an officer. That also speaks to why despite being an academy graduate he lacks the political correctness of a career officer (and remember how he feels about "these Academy hotshots.") Then bringing it all back home to the Victory, another novel reference helps us a bit! The WC3 novelization adds some specificity to Eisen's conversation about his posting: "I was communications officer on Victory's maiden voyage, my first assignment out of the Academy..."
So I will propose that the Victory entered service later than we'd previously thought, in the late 2640s.
Well, canonically the CF-105 Scimitar was in service for more than 140 years, and the first Dralthis came on-line about twenty years prior to that. And the first Fralthis came online around 2504 - about the same time Akwende drive technology was first developed in the Terran spheres of influence. The Arrow is probably fairly close in terms of overall length of service as well, though I'd be hard-pressed to provide a canonical precedent (probably the craft's appearance in the Academy cartoon is the best I could do).
Star*Soldier gives us early 2650s for the Arrow's introduction, too. Probably worth considering that there's a huge difference in terms of technological advancement in wartime. You jump from biplanes to early jets in a few years during World War II, versus aircraft designs that remain largely unchained for decades and decades today. (Actually the Scimitar is probably most notable in that it's the rare design that we know the Confederation actually /stopped/ using at a particular point. Though they were still serving with militia units will after that...)
I see the Scimitar kinda like the A-10 - a plane that everybody in the military derides except for the guys who fly them, and a design that just refuses to die.
It might actually be the reverse... almost all of the characters (yeah, yeah, Knight) who actually fly it do seem to genuinely hate the Scimitar. (It is interesting that it's treated as high tech on Wing Commander Academy, despite being at most only a few months before Wing Commander I... I get what they were going for, but wish they'd set the show earlier to make it work.)
I do agree with the OP that it's probably the Broadsword; serves reliably throughout the entire war and beyond.