Slanted Mezuzah - Now No One Is Happy?!

A Jew affixes a mezuzah to the doors of his house. Most mezuzos you'll see are on a diagonal. This is due to a difference of opinion between Rashi and Rabbeinu Tam. One says that the mezuzah is to be place completely horizontally while the other claims it should be placed vertically. In order to satisfy both opinions we compromise and put it on a slant. (רמ"א יו"ד סי' רפ"ט ס"ו)
Now, if the opinion of Rashi is to affix the mezuzah vertically, and that of Rabbeinu Tam is to do so horizontally, placing the mezuzah at a slant (neither vertically nor horizontally) is contrary to both opinions and seemingly futile?!
There are two explanations offered: a. There is a third opinion in the Gemarah that if one places the mezuzah diagonally it's unanimously kosher. The argument is only if vertical or horizontal is also valid, but both opinions agree that diagonal is certainly good.
b. The chief opinion is indeed like Rashi who holds that it should be affixed vertically; however, Rashi would hold that diagonal is also considered like vertical. Now, when one puts it diagonally, he is technically not putting it completely vertical either, so Rabbeinu Tam would not outrightly object either. Thus, we place it so making both opinions "happy."
שו"ת מנחת אלעזר ח"א סי' ל"ו ד"ה וגם
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Chilazon - A Plant?

The blue-like thread that the Torah tells us to attach to the tziztis is a derivative of the Chilazon snail. The exact definition of the Chilazon as well as the dye it produces was lost to us many years ago. Towards the turn of the nineteenth century, the Radziner Rebbe - R. Gershon Chanoch Heinich Leiner - researched the topic and wrote an entire book on the matter, claiming that he had found the snail. His chassidim wear the dye it produces until today.
R. Yitzchak Halevi Herzog - first chief Rabbi of the State of Israel - wrote his doctorate on the subject and concluded that it was most probably a different fish, but he couldn't conclude for sure on any specific specie. Until today, there is much debate on the subject.
It is interesting to note the Ra'avad's description of the Chilazon:
"...It is impossible to determine if the Chilazon is a fish or a plant. For it is alive and has movement, [yet] it does not move from its place for it is firmly planted in the ground..."
הקדמת הראב"ד לספר יצירה הנתיב השמיני
ועי' בשו"ת נודע ביהודה (תניינא) או"ח סי' ג' ובהערות שם
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Davening is Not an "Obligation"

Many of the mitzvos we do require a brachah prior to their fulfillment. Not all of them do however, and the Sages discuss at length the reasons for the lack of a brachah by each of these respective mitzvos.
One of these is tefillah. The common reason cited by many halachic works is the reason of given by the "Avudraham" (סוף דיני שמו"ע, הובא במג"א סי' ק"ו סק"ד): Tefillah does not have a "קצבה - a set amount/time," and is thus absolved of a brachah.
What exactly does this mean - why does the lack of קצבה absolve the need for a brachah?
The Gemara (ברכות כח, ב) says that one should not make their tefillos "set," i.e. it should not be a the product of a rote obligation, rather a sincere supplication from the heart. This is why one does not make a brachah prior, for the implication of blessing beforehand is that one is "fulfilling an obligation" and "doing his due duty," which we do not wish to convey. This is the true meaning of the words of the Avudraham: there is no blessing because it should be something that is not set and obligatory.
בגדי ישע על המג"א סי' ק"ו סק"ד
ועי' פמ"ג פתיחה כללות להל' תפילה בסופו טעם אחר
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Watch Where You Look

Before receiving the Torah, there were preparatory days wherein the Jews got themselves ready for the holy day. Hashem instructed Moshe to tell the Jews not to ascend the mountain; a boundary was set up which the Jews were not to cross. They were severely warned not to do this. The second time Moshe was preparing to receive the luchos, Hashem gave similar instructions, adding that no person should be present when he was to ascend, and even animal should not graze there.
From Hashem's instructions that upon ascending the mountain the animals should not be around, the Rokeach writes that this hints to the following idea: On the day we initiate a child to learning from the holy Torah, we cover him so he shouldn't see any dogs.
רוקח הל' שבועות ריש סי' רצ"ו
ועי' בלקו"ש חכ"ה ע' 310
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Using a Magnifying Glass for Halachah

The Aruch Hashulchan writes:
"There are those that say in the name of scientists that if one looks through a magnifying glass, they will see many insects in vinegar. Now, with vinegar, there is no problem... but I hear that all water, specifically rain water, is full of microscopic insects that are not visible to the naked eye. In my youth, I heard from someone that traveled far and used a microscope that enlarged the object thousands of times, and he saw all these insects. If so, how can we drink this water?
The truth is that the Torah does not forbid that which the naked eye cannot see, for the Torah was not given to angels. If one does not say so, now are there not scholars who say that the air is also filled with microscopic insects and when a person opens his mouth, he swallows many of them?! Surely they are speaking nonsense! Even if it is indeed so, being that the naked eye doesn't see them, it is nothing..."
He says the same thing about microscopic scales on fish - it still doesn't make them kosher:
"...Know, it is given, that with anything that needs to be visible, seeing it through a magnifying glass does not qualify; the naked eye must be able to see it. This holds true with anything in the entire Torah that needs to be visible."
ערוך השולחן יו"ד סי' פ"ד סל"ו וסי' פ"ג סט"ו
ועי' חכמת אדם כלל ל"ח בבינת אדם סקמ"ט
ועי' טוב טעם ודעת (למו"ר שלמה קלוגער) מה"ת קו"א (הל' טריפות) תשובה נ"ג
See here, and here

Righteous Women

The Kiyor in the Mishkan was fashioned from what the Torah calls "ma'aros hatzovos - mirrors of the women who had set up the legions."
Rashi explains that these mirrors were brought to Moshe by the women of the time. Moshe was disturbed with this donation, as they were used in Egypt to entice their husbands to have children. Hashem instructed him that this was indeed a virtuous act and most dear to Him; Moshe accepted them and the Kiyor was constructed.
R. Avraham Ibn Ezra takes a different approach:
"The way of all women is to beautify themselves by looking at their faces each morning with a copper or glass mirror and fixing the hair style on their head. This is referred to in Sefer Yeshayah, for the custom of Israel is as the custom of Ishmael until today. There were righteous women is Israel, servants of G-d who cast away the lures and pleasures of this world and donated their mirrors, for they did not need to beautify themselves. Rather, they would come every day to the doorway of the Mishkan to pray and hear the words of G-d's commandments."
פי' ראב"ע שמות לח, ח
ועי' רמב"ן שם ובתולדות יצחק שם (ועי' בסיום דבריו שהספור במשכן וכליו וצרותו אע"פ שאין בית המקדש קיים מצוה גדולה ושכרה גדול)

Help Her Out

Just as a man is supposed to help his wife with lighting Shabbos candles by preparing the candles, etc. he is supposed to ensure that the lights in all the other rooms are lit. The woman acts as his shliach when she lights, and as such, he is responsible for the other rooms that she doesn't take care of. So, erev Shabbos, the man goes around the house and makes sure that all lights that need to be on are on. However, a brachah is not made; his wife's brachah takes care of that.
שו"ע הרב סי' רס"ג ס"ה, ס"ט
ועי' אליה רבה סי' רס"ג סקט"ו ובמה שנסמן שם
וע' קו"א בשו"ע הרב שם סק"ב