Eagle ground consistency
The "ground islands" as you call them are the parts of the design and will cover the space not used by the autorouter for other signals. So you have the following factors playing role here:


Quality of package layout. You must think and imagine what would be the best layout of the components on the board - for connectivity, for EMI, for connector placement, for mounting hole location etc. The package layout will identify how well you can route signals, and the shape of the "islands" and their interconnectivity;
Autorouter. People used not to like it, however my personal opinion is that it is good to see how well you have laid components out on the board. In any case, the job autorouter does is not of the best, and you usually choose to route manually keeping in mind things autorouter did on the layout. If you can not route properly, most probably you must return to step 1 and change layout of the packages on the board.
Connecting ground planes/islands. While you can rely on the polygons connecting the ground pads and pins, I strongly advise to connect them explicitly using Route with required thickness - this way you will 100% know through DRC that you do not miss any conductor sizes and widths. You will use through-hole pads or vias connecting ground polygons at both sides of the board.
Further, if there's space within polygon area but it is not covered by the copper, this means that EAGLE can not find a way to route ground in that space. You can use via assigned with ground signal name from another side of the board;
You should also mind settings of the polygons - thermals, isolation, rank, and ensure you comply to the PCB board manufacturer and assembly house requirements.