Fighter damage bonus combines with cleaving for a nice little power-up for fighters compared to B/X. By the book character generation, with 5 sets of 3d6 in order but with point trade-offs, makes seeing fighters with 18 strength more common than I expected, which synergizes with cleave as well. None of that should trip you up inherently, it's just a way of keeping fighters in the game as spellcasters acquire higher level spells. (I note that weapon mastery in BECMI and weapon specialization in AD&D were moves in the same direction.) What did trip me up once was the player damage output when running published non-ACKS OSR adventures. Low level monsters statted in other rule sets can basically be run as is, with AC converted on the fly, but higher hit dice monsters felt a little weak. As time allows, run them through ACKS monster creation rules - you'll see higher HD monsters should usually deal more damage or have more attacks than in other old school rulesets.
I got a little bit of pushback from my new-school players on action declarations for casting spells and withdrawing from combat. Those feel restrictive, but they do play an important part in balancing combat. That was partly my fault, as I default to only teaching rules as they come up, so if I were starting again I would lay those out at the very start, possibly with a handout sheet, so no one was surprised.
the death and dismemberment table is going to figure in heavily when PCs get dropped below 0, and it won't always be fatal (but it's usually grisly).
I played in a B/X Barrowmaze game some time before running ACKS, and dead at 0 hp was quite brutal on the PCs starting out. Between the Mortal Wounds table at 0/below, and Restore Life and Limb listing at 500 gp (if the party can find a caster in time), ACKS felt surprisingly casualty-light to me.
And lastly, are there any commonly accepted house rules that people use to smooth out the rough spots?
I ran for an open table, and what I should have done from the outset but only figured out late in the game, was to make one adventure session or dungeon delve per month of campaign calendar time an explicit meta-game house rule. That makes a nice clean unit of time to track downtime activities for absent players/non-adventuring characters. And has the side benefit of allowing you to figure out a standard living expenses chart, instead of looking up lodging and meals each time the party is in town.
The rules sort of steer towards an adventure a month anyway when you start encountering the Mortal Wounds and Tampering with Mortality tables, or gathering rumors, but it's a soft push, and my players' tendency was to push onward whenever they could, which made tracking time and downtime activities more of a hassle than it need to be for me.
Of course if you're running for a fixed group with good attendance this becomes less important, but I would still consider it for a game centered on dungeon delves.