How do you handle tiny islands when cutting layered water maps?

Don't delete the small stuff. What works for me is adding tiny bridges, basically little tabs maybe a couple kerf widths wide, connecting each island to the main water shape. You do this in your design software by drawing a thin rectangle over the cut line where the island sits closest to the shoreline. The island stays attached to the big sheet during the cut, no warping, no lost specks, and then you snip the tabs off with flush cutters after. A quick sanding on the tab spot and you can't tell it was there. The downside is the bridge leaves a tiny notch in the island outline, so put it on the side facing away from where people will look.

If a piece is too far from shore to bridge, cut it on top of low tack masking tape laid on the bed. The tape holds everything in place til you lift the whole sheet off, and you can carry the island over to your work bench still stuck to the tape, glue it, then peel the tape off. Works way better than chasing confetti around a honeycomb bed.

On the alignment question, that mismatch between layers two and three is almost always a glue up issue, not a file issue, assuming you cut everything from the same file set. What I do is put dowel holes or small registration notches in the same corner spot of every layer, then glue up over a printout of the bottom layer so I can eyeball the shoreline while each piece goes down. Work from the bottom up, one layer at a time, and let each one set before adding the next. Trying to align wet layers by eye is how you get that drift you're describing.

One other thing, check that your plywood is actually flat before cutting. Slightly cupped stock will shift things around on the bed and between layers even when your files are perfect. Weigh it down flat for a day if it's warped and you'll save yourself a headache.

One thing I do on top of what's been said is engrave tiny crosshair marks on the underside of each layer, positioned so they land inside a solid area of the layer below when you stack them. Then when I'm gluing I hold the piece up to a strong light from behind and I can see the crosshairs through the plywood and line them up before the glue grabs. Sounds fussy but it takes two minutes to add to the file and it has saved me from more than one crooked layer. Also check that all your sheets are actually the same thickness, because cheap plywood varies more than the label claims and a hair of difference shows up fast once you stack three or four layers.

For the realy tiny ones I stopped cutting them through at all. I engrave them into the top water layer instead, just a shallow pass so they read as little rocks and shoals. Lost a whole afternoon's worth of specks on my first river map before I switched. Anything bigger than about a pencil eraser still gets cut and glued, the rest is just part of the layer now and honestly the map looks better for it.

On the glue up, I keep a damp rag next to me and wipe squeeze out right away, becuase dried glue bumps will hold the next layer up slightly and you get that same drift without realizing it.

I have to push back on the masking tape idea though. Every time I've tried cutting small pieces over tape, the tape bonds to the underside of the ply and peeling it off pulls fibers or curls the thin bits worse than they'd ever warp on the bed. On fingernail sized stuff you end up with a sticky, splintered mess. What worked for me instead was laying a sacrificial sheet of cheap thin ply or even heavy card under the good layer, so the islands stay sitting in thier cut holes and nothing moves. You lift the whole sandwich off in one piece and seperate it at the bench. Tape also seems to leave residue on birch face veneer that shows up under finish, or is that just my tape being garbage?

Update: tried the little tab trick and every island made it through the cut, which felt great until I noticed you can faintly see the slots where the tabs sit once the water layers are glued. Sanded and recoated but they still catch the light a bit. Do you just place tabs where a wave or shoreline detail hides them, or am I overthinking it? Also love the crosshair idea but my ply is too thick to see light through, ended up using my phone flashlight from underneath.