fenny,
The main effect of a higher filter order is that the roll-off is much quicker (i.e., there are fewer frequencies between the pass band and the stop band). Depending on the type of filter that you use, there may be more phase delay with higher orders. Some filters are designed for phase delay (I think elliptical and Chebyshev are phase delay filters), but some filters will not give anymore phase delay with higher orders (e.g. a Butterworth filter). But there aren't really any "side effects" to having higher orders other than possibly longer processing times. I hope this answers your questions!
Tyler S