The dado is the least dramatic joint in casework. You cut a channel, drop a shelf in, and the shelf is located. It's not going anywhere. It contributes rigidity, tells the eye where the shelf belongs, and does its job without needing to be impressive.
That's exactly why people get careless with it.
There are three ways a dado goes wrong, and none of them happen at the router. They happen in the five minutes before you turn the machine on.
Depth. The rule is one-third of the panel thickness. For 3/4" stock, that's 1/4". No more, no less. Cut to half the thickness and you've weakened the panel at the exact point it's taking the shelf load. Cut too shallow and you've built an expensive glue joint — the shelf leans against wet adhesive instead of sitting in geometry.
Plans often show a depth. Use the one-third rule as a check anyway. If it deviates significantly, ask why before cutting.
Fit. A dado should fit snug-sliding. Two thumbs of deliberate pressure slides the shelf in. The shelf resists coming out when you tip the panel. No mallet.
This matters most during glue-up, which is the worst time to find out you got it wrong. A mallet-fit joint dry becomes a nightmare wet: glue raises the grain, wood swells, you're beating a wet shelf into a wet channel while the clock is running. A shelf that slid in cleanly dry will seat again with glue applied. A shelf that required force dry will stick halfway.
If the fit is too tight: plane the shelf, not the dado. A few passes on the long-grain faces with a hand plane is faster and more controllable than any other fix. Never widen the dado to rescue a tight shelf. You can't undo slop.
Dimension. The number on your plan is not the thickness of your shelf.
Nominal 3/4" hardwood plywood is typically 23/32". Baltic birch is metric, usually closer to 11/16". The variation between suppliers, between lots, between the sheet you bought this year and the sheet you bought last year means "3/4 inch" is a range, not a measurement.
The protocol: rip a scrap from the same sheet as your shelf stock, measure it with calipers, set your dado stack or router fence to that actual number, then cut a test dado in scrap before touching the carcass. This takes five minutes. The rework it prevents takes hours. It's the most common fit problem in dado work, and it has nothing to do with skill — just the assumption that nominal means actual.
Two other things worth knowing.
Cross-grain dadoes tear out at the entry and exit points if you let them. Clamp a backer board at the exit edge before the first pass, or score the layout lines with a marking knife. The channel will be clean. The edges are where sloppiness shows.
In wide solid-wood panels, a cross-grain dado constrains seasonal movement. A fixed shelf glued into dadoes on both sides of a 24"-wide solid-wood carcass will fight the panels as they expand and contract. Either don't glue it, or use plywood where movement isn't a variable.
The dado is structurally simple. The material you're cutting it into isn't.
Every casework build has a moment when the shelves go in and the thing becomes furniture. That's the dado's contribution. It locates, supports, and stiffens. It doesn't ask for credit. Make it right before the router starts, and it won't ask for anything else.