It appears to be laced correctly (more photos would help verify) but a I agree that the wasn't built properly. The spokes need to be better seated at the flange. The process will certainly require retensioning and truing, and it is probably better to do it now instead of waiting for spokes to break and needing a more expensive rebuild.

I would also also guess that either the tension is very low, or it will be after riding it. Nothing is worse for a spoke than riding at a tension so low that the spoke will go slack. I would get it looked at by a competent wheel builder ASAP. I will cost far less to do it now than after the wheel has failed.