Authentic Mexican cooking varies enormously by region — the mole negro of Oaxaca shares almost nothing with the cochinita pibil of the Yucatán. The first sign of an authentic restaurant is that it claims a regional identity, not just "Mexican food."
Look for handmade tortillas. A corn tortilla made to order — pressed and cooked on the comal in front of you — has a texture and flavor that no factory tortilla replicates. If you can see the tortilla press, that's a very good sign.
The salsa should have complexity. An authentic Mexican salsa is smoky, often charred, sometimes fruity, always layered. If the only salsa on the table tastes like tomato paste with jalapeño, that's a fusion shortcut.
Check whether the menu includes dishes you don't recognize. Mole de olla, chiles en nogada, enfrijoladas, tlayudas — regional dishes that don't appear on generic menus tell you the kitchen goes beyond the top ten crowd-pleasers.
The drinking culture also signals authenticity. A genuine Mexican restaurant will have mezcal by small producers alongside mainstream tequila, fresh agua frescas made daily (hibiscus, tamarind, horchata), and perhaps tepache (fermented pineapple) if the kitchen is truly cooking from scratch.
Finally, check the clientele. If Mexican families are regulars, the kitchen has already passed the most demanding test.