I have flown to Dubai on Saudi and within the country. The last time I flew international with Saudi it was on a huge 747. They fly them to Dubai as the Saudis tend to escape on the weekends for a little R&R and needless to say it was packed. Mind you I was happy to be leaving, per the whole monster cockroach incident. So I sat down next to a covered lady and her child. Two seats, the baby was on her lap. After take off, she asked me to hold the baby while she went to the bathroom. Off came the abaya(the required garment that all Saudi women must wear). The joys of leaving Saudi.. Anyway, we were talking about Dubai and her family when the ceiling started leaking on the girl across the isle from me. It wasn't condensation, but some kind of black liquid. God knows what it was.
Saying, that Saudi Airlines domestically has improved dramatically and the service is very good. Also, I always feel extremely safe and welcomed in the country. I am American and never have felt worried about my security and have travelled extensively throughout the country.

Also, one recommendation. I am assuming you will be with your sponsor on this trip, have him take you to this restaurant/cafe "waterfalls". It is a great sheesa (flavored tobacco) place and has excellent Lebanese food. Definitely go there and experience the culture. It's great.

Enjoy,

Billman