Error in Schematics or am I missing something?

If the intent is to alternately light the LEDs when the push-button switch is actuated and released, then the schematic is wrong. The positive from the battery must connect to the moving contact of the relay, which is pin 5. The anode of the left-side LED on the schematic must connect to the normally-closed contact, which is pin 3. The breadboard drawing is correct.

BTW, dual in-line package (DIP) pins are numbered counter-clockwise starting at pin 1 in the upper left corner, continuing down to pin 8 in the lower left, then continuing from pin 9 in the lower right and back up the right side to pin 16 in the upper right... all this looking down on the relay package from the top (relay pins pointing down into the breadboard. There is usually a dot or a "U"-shaped notch on the package to identify which end to start the pin numbering from. Same pin numbering scheme applies to any size DIP package... 4-pin, 6-pin, 8-pin, 14-pin, 16-pin... etc. It gets really hard to count when the pins number twenty or more. Gets even worse when the package is surface mount and contacts are on all four edges. Becomes impossible when the package is a ball-grid array with contacts on the bottom. But you aren't there yet, so don't worry 'bout it.

 

Yes.