Your polygons look a bit out of alignment. They will need to be contiguous to be dissolved so check for any gaps. Manually using the merge option on the editor toolbar should put them all together but still leave the small gaps. After the merge you could add new features off the same dataset to cover them up, then merge the two together again. Also performing a union to itself with the no gaps option could do it. The integrate tool may also work, but beware this will alter your entire dataset with little control over the process. Do this in edit mode or make a copy of your dataset before trying integrate as a last resort.
