Would it cause any problems if COM on one side of the main unit contact input DI is shared?

If you share (wire) the DI's COM there will be no isolation between the DI's inputs, but otherwise there should be no problem.

YS1310

Indicator with Alarms with space saving mounting and streamlined design
YS1350/YS1360

Manual Setters with low maintenance and industry-proven results
YS1500

User-friendly design with AC/DC dual power supply
YS1700

Programmable Indicating Controller with high reliability for multiple applications