The situation in Egypt does not look dire at this moment, but it does look very serious. Given the speed with which events can move, the situation could change dramatically for the worse in hours or days.
Pursuant to the 1979 peace treaty between Israel and Egypt, Israel withdrew from the Sinai peninsula which it had captured in 1967. The Sinai provided a strategic depth which allowed Israel to withstand the surprise Egyptian attack in 1973.
A key element of the peace treaty was restrictions on the quantity and quality of Egyptian troops and weaponry in Sinai, so that Israel did not need to worry about the well-equipped and well-trained Egyptian army sitting on its border. Other aspects included a right of free passage through the Suez canal and the waterways south of Israel and east of the Sinai such as the Strait of Tiran and the Gulf of Aqaba. It was a blockade of these waterways by Eqypt which sparked the 1967 war.
Unfortunately, while the peace treaty contemplated a normalization of civilian relations between the countries, such normalization never took place on the Egyptian side. Egyptian society, particularly the large segment represented by the Muslim Brotherhood, still does not accept Israel and largely boycotts Israel in civilian affairs. Agitation against Israel and Jews is common in Egypt.
If the Mubarek government falls, as happened quickly to the government in Tunisia, the Israelis rightly would be worried about the impact on the peace treaty. If an Islamist government were to take hold in Egypt, there is no telling how the situation in the Sinai could deteriorate. The role of the Egyptian military as a political force in maintaining the military aspects of the peace treaty would be paramount.
While we are not there yet, I can see scenarios by which a new government in Egypt disavowed the peace treaty either explicitly or by actions. If Egypt moved forces into the Sinai beyond that permitted by the peace treaty or breached the other covenants such as free passage through the Suez canal, Israel would have a hard choice of moving back into Sinai or allowing the establishment of yet another hostile front on its borders, adding to the Hezbollah controlled Lebanon, the Hamas controlled Gaza, and Syria.
Eqypt is not Tunisia. The effects of Mubarek falling without a successor willing to honor its commitments under the peace treaty with Israel could spark a war.
Update: There is a another distabilizing possibility, that the new Egyptian government doesn’t do anything that violates the peace treaty itself, but ceases trying to stem the flow of weapons into Gaza from Egyptian territory.