One other message to take with us from Shavuot is אחדות, or Jewish unity. The Pasuk says, ויחן ישראל כנגד ההר, Israel dwelled opposite the mountain. It should have said ויחנו, in the plural.
The explanation is כאיש אחד בלב אחד, as one man with one heart. This teaches that on Mount Sinai there was incredible unity among the Jewish people. This was certainly important at that moment of Divine revelation when we received the Torah.
Some say this is the explanation of the famous story of the non-Jew who asked to be taught the Torah on רגל אחד, one foot. The play on words of רגל is that it could be referring to the שלוש רגלים. The non-Jew is asking what the meaning of the רגל of Shavuot was all about. Succot was about dwelling in a Succa and Pesach was about Matza and the Seder. What was Shavuot about? Hillel answered that the message of Shavuot was ואהבת לרעך כמוך, love your neighbor as yourself. The rest is commentary. We need to take this feeling of Achdut and love into the summer months ahead.