1) You have layer violations (crossed out pads)
2) Red is top layer
3) Blue is bottom layer
4) You have unrouted airwires
Please do the following: Turn off all layers except the bottom (blue) layer. Print it, mark "black" in the print dialog.
You should get a normal looking, but obviously incorrect board. That will confirm the errors are in the board layout, not something funny with Eagle.
If you attach your board file I will work with it. ETO allows Eagle BRD files.
It appears that as you were making the layout, you changed from one signal layer to the other. For example, from red to blue. You then had pads on one layer and tried to connect to nets on the other without a via. That won't work. Eagle won't allow a valid connection to be drawn that cannot be made in reality.
John