Can your simulation software apply unique designators to the parts in your schematic? There are a few comments that I would like to make but it is difficult to do so without being able to call out an individual part.
But one comments about somethings that might simulate OK, but may not work properly in hardware is:
Floating inputs. (neither high nor low) Particularly when you use diodes and switches in your logic path. For example, two of the CD4510 clock inputs that are feed from a switch and a diode. The counter connected to the open pole of the switch will always be floating. The counter connected to the closed side of the switch will be floating when the state on the other side of the two diodes feeding that net is LOW (the diodes are not froward biased and are therefore open connections). If your circuit is simulating OK, then the software is set to treat a floating node is a logic LOW. In real hardware you need to ensure that a floating input is in a KNOWN default state. Use a resistor on each of these two inputs to ensure the state is LOW except when they are driven HIGH. There are other unconnected pins that are floating. If they never need to change state then they can be tied directly to the supply rail, depending on which state they need to be.
I think that most designers would not use diodes or mechanical switches in the signal path. Their function could be accomplished much more cleanly with logic elements.
As for for your LED question, it depends on what LED you are using and how bright you want it to be. The 1.6 volts that you see is the forward voltage of the LED itself. This voltage varies from part to part for different reasons. Including operating current, part temperature and color, with color making the largest difference. The brightness vs current varies across a huge range. One part may be brighter with 0.5 mA than another is at 20mA. You need to chose your LED, then choose a current limiting resistor that sets the brightness where you want it to be. You also need limiting resistors between the CD5411 drivers and the 7-segment displays.