The Haggadah of Passover contains many deep secrets. Here are some of them:
1. The hidden clue in מצרים, reflects the role of water in Egypt. If you move over the first letter, the מ, two places to the left, you now have the words צר מים (distress of water). This is pertinent considering that the Egyptians threw Jewish male babies into the Nile, and that the water of the Egyptians turned to blood, and that the entire Egyptian army drowned in the Red Sea.
2. Moses, משׁה is mentioned in the Haggadah only one time and even then it's in the capacity of Hashem's servant. Hashem wants us to know that it was only He that redeemed us from Egypt. But the name משׁה is hidden secretly. But where? Look at the section where the Haggadah states that it was G-d that took us out, not מלאך (an angel), and not שׂרף (a seraph), and finally not השׁליח (a messenger). Notice that the first letters of these 3 words spell משׁה.
3. According to Rabbi Akiva, there were 50 plagues in Egypt, representing the power of G-d's full hand, and another 250 plagues at the Red Sea, for a total of 300. These plagues represented the power of G-d. So it's no wonder that the atbash of Hashem's yud kay vav kay name is 300.
4. This is the "bread of affliction" הא לחמא עניא. This bread of affliction, or matzah, humbles us. Hashem takes notice and remembers the humble, the oppressed, the widows, orphans and the distressed. This "bread of affliction" has the same 216 gematria as ויקוק פּקד, "And Hashem Remembered.
5. In the verse צא ולמד, "Go and learn" Lavan, the Aramean, is mentioned as the example of one who hated us so that he planned to destroy the entire Jewish Nation. The atbash of Aramean, הארמי, is 543. This represents the modern version of such hatred. For 543 is the combined value of Russia רוסיה, and Iran איראן.