No there should be no problems using drives of different spin rates in the same server. The only difference is that one drive might be slower than the other so there will be a little more latency when accessing the slower drive's mount points.
*Note: This assumes the drives will not be used in a RAID, which the questioner mentioned. Even if two drives of different specs are used in a RAID, this will not necessarily cause problems in all cases but will just cause the higher spec drive to perform like the slower drive. So essentially you are wasting money on an expensive drive when paired with a cheap drive in a RAID array, but it will be functional.
2Your answer should repeat the stipulation that the HDDs will not be used in a RAID configuration. Otherwise you're making a generalization that is not always true, especially for servers, where RAID is typically found. – sawdust – 2013-07-18T21:29:14.213