There's quite a few in that 7 minute video so I'm just going to go through this in list form and hopefully I'll get all the ones you were interested in:

1. As soon as the music starts you see a red cloth with a Star of David on it, later on you see it spread on a large table. That's where the Torah goes, the cloth protects the delicate scrolls from tears and dirt. Sometimes this can double as the curtain hung in front of the Torah ark as well.
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2. At 0:24 the view flashes to a hanging gold object and then to another object. The first is the sanctuary lamp which holds the Eternal Flame. This flame is kept lit at all times and is usually positioned relative to the Torah ark so that the congregation sees it in front of the ark. The flame symbolizes God's presence, thus it is NEVER extinguished. Many nowadays may even be electrical, all that counts is that it never goes out. In Israel it's not uncommon for a synagogues eternal flame to have at least 2 or 3 ways of keeping it up during power and/or gas loss.
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3. at 0:25 the second object you see in quick succession is a Torah ark. The two tablets on top are actually a film-blooper, the Torah is quite explicitly clear on the dimensions and shape of the ten commandments and they were actually large square blocks rather than the popular double-tombstone shape.
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4. 0:25-0:26 this is the temple's Menorah. Not a Hanukkia, which is a TYPE of Menorah. It holds seven candles and dates back to the ancient temple of Jerusalem. Traditionally this, and not the Magen David, is the true symbol of judaism. The shape has a lot of mystic meanings behind it but suffice to say it is quite important.
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5. 0:29 This is a shot of the second half of a Torah scroll. Torahs are scrolls, not books, written (and read) in Hebrew from right to left. You are more likely than not already familiar with it's contents, which are known as the "Old Testament" to gentiles.
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6. Throughout the video you see the men have strings dangling from beneath their clothes. These are the Tzit-Tzit of their Tallit Katan. A miniature version of the larger ordinary Tallit prayer shawls worn when praying, specially designed to fit under a man's clothing. In short: It's a holy jewish wifebeater. When hung up to dry after being washed it looks like a sheet with a hole in the middle... sound familiar?
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7. 5:45-5:50 the camera goes back through the Menorah, Eternal Flame, Torah Ark, the place where the Torah is set while being read from, and some more traditional Jewish artwork.