IMO (as someone who still plays 1E, though recently I've been moving even further back, to white-box OD&D) 1st edition feel can be defined as a matter of friendly competition in an atmosphere of mutual trust. The players expect the DM to challenge them, to do everything he can to kill their characters and generally make life difficult for them, but they also trust him to "play fair" and to reward (rather than resent or punish) clever play. Likewise the DM expects that the players are going to do everything they can to keep their characters alive and get as much treasure and experience as possible at the expense of his carefully designed monsters and traps, but he also trusts them to accept the rules and assumptions of the game in their intended spirit (i.e. not to be 'munchkins' or rules-lawyers).

With this relationship between DM and players questions of 'logic' and verisimilitude are completely irrelevant, both in rules (a set of defined and consistent rules isn't needed for every circumstance because the DM is trusted to use his common sense, judgment, and sense of fairness to adjudicate any situation that isn't covered (or isn't covered satisfactorily) by the RAW -- remember that in the earliest days the DM was typically called either 'referee' or 'judge') and in setting (things like motivations and ecology don't matter because it's obvious why the monsters and traps are there and function in the way they do -- to challenge the players -- and equally obvious why the characters are facing them -- because the players want to be challenged by the DM (and, if they successfully face that challenge, be rewarded)). Games in those days weren't primarily about developing complex characters and telling compelling stories, nor were they primarily about modeling a fictional or alternate reality in any consistent or logical manner. Yes both of those elements played into the experience, but primarily the game was simply about a group of players sitting across the table from a DM and matching wits with him in friendly competition in an atmosphere of mutual trust.

Of course it didn't always work out that way -- the competition wasn't always friendly, which led to an erosion of trust -- players convinced that the DM was 'out to get them,' DMs convinced that the players were munchkin powergamers who needed to be put in their place -- and the rules, which depended on this balance of mutual trust, weren't able to handle this (there are no 'checks and balances' built into the 1E rules -- as much as players can exploit and abuse them to create super-characters, they're still ultimately subject to DM fiat with no recourse except to quit the game and play with a different DM). Thus the 3E rules are more tightly defined and more carefully balanced to (at least theoretically) prevent the worst excesses of both player munchkinism and DM arbitrariness. But a consequence of this is that the rules tended to become more mechanistic and less freewheeling -- because the players know that there are rules that define most things they're more likely to think in terms of those rules rather than just trusting the DM and going along in the spirit of friendly competition -- and thus the 'feel' tends to be different.

And that, therefore, is the key to first edition feel IMO -- a lack of concern with mechanistic balance and logic, replaced a willingness to trust the DM and assume not that he's out to kill your character out of spite but rather that he's out to challenge your character because it's a game, a competition. If the DM decides that teleportation spells don't work in this dungeon, or that this particular monster is immune to every form of attack except for two special weapons that happen to be hidden nearby, or that a particular trap doesn't allow a saving throw, don't question the logic or balance or 'fairness,' but rather accept that these are the terms that the DM has set for this particular challenge and 'step on up' to face it -- knowing that if you're successful you're likely to get a rich reward (and either way you'll at least have a fun evening of play). Friendly competition in an atmosphere of mutual trust; that's what first edition feel is all about.