Clustering, Mixed Data Set with Ordinal and Nominal Scale Data
Yes, it causes almost no trouble. The only caution you must have is the possibility of having a regular ordinality where the ordinality is actually irregular. For example, having shirt size 1, 2 and 3 but the size "3" is not three times bigger than size "1".
The dummy variable creation is a very valid approach when having categorical variables in your dataset, not only for clustering but for almost every model you could construct.