What skills are most important for applications in Saudi Arabia?

Should respect every religion and country laws. Not only about Saudi Arabia. 

First of all you need to understand nature of the Job you seeking and then accordingly you can add or upgrade your skills. 

With the development of the country, the employers are not only looking for experienced and skilled professionals but also highlighted the motivation, the responsibility, the respect and the passion that they must have.

Employers permit recruitment of foreign nationals who bring in specialist skills where there is a shortage. The skills that employers are looking for are loyalty, hardworking, time management,commitment, ability to work in a team, English language, and computer literacy.

Job Description Matching Qualification

Relevant Experience

Disciplined

Multi Language 

Religion is for God and the homeland for all

Wish I was in Saudi to answer your question but i guess is the question of principles and following them.