The kanji for "Himekaidou" mean "princess", "sea/beach" and "crabapple tree" respectively. "Himekaidou" itself is a kind of toringo crabapple. (Malus sieboldii).
"Hime kaidou" also refers to a side-road, often taken by women or travelers who wanted to avoid thieves.
Hatate's clothes have a lot of purple color. Purple color symbolizes "mystic" or "royalty". "Mystic" might be associated with her spiritual powers. "Royalty" might refer to "Himekaidou" - princess. Also purple represents the deadly sin pride.
Her spirit camera looks like some sort of cell phone. Since she is "putting in" keywords it makes sense in a way.
A silhouette of Hatate occupies the front of Double Spoiler's jewel case.
She admitted that she had seen the ocean before, in the comment of Double Spoiler. Considering the fact that the sealing of Gensokyo is estimated to be happened in 1885 A.D., it is likely that she is over than at least 100 years old.
In the Japanese fanbase she has been associated with scallops (ほたて hotate), due to the similarity with her name (はたて).
The pattern on Hatate's skirt is identical to the "missing texture" pattern in Half-Life 2 and other Source-based games, which has lead to jokes among fans.