I received the following in an email, and am re-posting with permission.
These notes come from a memorial service held recently for Rav Shlomo Zalman Auerbach zt"l, in Raanana. They are not my own, and I have not edited them. I have only made one change, noted in the text, where I felt there was a significant typo.
1. Any question that had a technical side he worked to understand the science and not just be given facts from some pseudo-expert. He had contact with many top scientists and doctors in Israel. One of the fascinating stories concerned the debate over brain death.
Rav Shlomo Zalman felt that if a lady could give birth after being brain dead she was not dead according to halacha. To ascertain this he designed an operation where they cut off the head of a pregnant sheep (so that the sheep was certainly dead) and waited about 1/2 an hour and verified that the fetus was still alive. Dr. Steinberg claimed that to his knowledge this was the only surgery carried out to verify a halacha. Rav Shlomo Zalman agreed he was wrong. He stated he was sorry he didn't write “in my humble opinion” (le-aniyat da-ati) in the original teshuva because then his opinion would be wrong. Since he stated it categorically he was now a liar.
Besides his sefer on electricity he wrote a lengthy teshuva on using the Frigidaire. He didn't publish it because he didn't have the money. Later in life when he could afford it he felt the technology had changed and there was no purpose in the original teshuva.
2. On the birthday of his physician he gave him a copy of Orot Hateshuva from R. Kook. When R. Lau became chief rabbi Rav Shlomo Zalman told him to make sure to continue the "heter mechira" of the chief rabbinate.
3. He always traveled by bus from his home to the yeshiva. Once a non-tzenuah woman sat next to him. A minute or two later he rang the bell and got off the bus. He then got the next bus (or walked) to the yeshiva. When asked about this he said that he could not sit next to the woman the way she was dressed. On the other hand, to get up and stand in the aisle would be an obvious embarrassment to the woman. So his only choice was to pretend he was getting off anyway.
Later in life the yeshiva insisted on sending a cab to pick him up. Rav Shlomo Zalman always used the opportunity to talk to the cab driver so he wouldn't feel just like a chauffeur.
He always attended the shabbat teshuva and shabbat hagadol derashot of R. Kulitz in the local Gra shul eben though R. Kulitz was many years his junior.
4. R. Lau mentioned that during the funeral of Rav Shlomo Zalman (R. Lau was then chief rabbi) he received a phone call from a reporter in a helicopter asking who was this person that 300,000 people came out for. R. Lau answered that part of his greatness was precisely that many people did not know anything about him. He refused to go to any event with a political overtone and was accepted by all the communities.
5. He always recited "birchat ha-ilanot" in the garden of a widow who had 2 trees. One year one of the trees withered and they suggested going to another yard. He insisted on returning to the original yard. He explained that having 2 trees is a hiddur while disappointing the widow is a de-oraita.
Later in life he once didn't go to shul for selichot erev Rosh Hashana which is a special selichot, because he was not feeling well. Later in the day he walked up 4 flights of stairs to visit several elderly gentlemen. When asked he explained that G-d realized he was exhausted and would excuse him for not coming to shul for selichot. However, the elederly people who he always visited would feel that he was not intereste din them if he didn't come.
6. He always came to shul 10-15 minutes before davening started and would use the time to look at the siddur and not learn.
He made appointments and insisted that people keep them exactly. The time set was not always at "round" times.
Dr. Steinberg said he always came 1-2 minutes before the time. Not too early to disturb Rav Shlomo Zalman and certainly once [I believe this should be “not” - MT] late. Once when he came Rav Shlomo Zalman was at the door waiting for him. When asked Rav Shlomo Zalman explained that he had trouble hearing the dorrbell and didn't want Dr. Steinberg to wait.
When he was mesader kiddushin he insisted that the chupa start at the time announced in the invitation. He said that to start late was stealing people's time
7. Once in a written question he was addressed with an assortment of titles. He answered on the same page and crossed out all the titles except for "HaRav HaGaon". When asked why he left that one he explained that everyone is called by that title and so it has no meaning.
8. He read the megillah in a loud voice for his mother who was hard of hearing. One year he asked his son to take over. Afterwards the son mentioned that he didn't think his grandmother had heard enough to be "yotzei". Rav Shlomo Zalman answered that he always knew his mother was not "yotzei". He did it so that she would feel good not for the mitzva of hearing the megillah.
9. Rav Shlomo Zalman was a strong backer of backing buying sheviit products from observant farmers who kept shemitta either in Gush Katif or through the various halachic ways. One year some people forged a letter that he said one should only buy produce of Gentiles. He was very upset and explained that he wasn't bothered by any personal insult that the forged his opinion. He was upset that they were stealing the livelihood of Tzaddikim.
Obviously, Rav Shlomo Zalman was unique even among gedolim.