Rav Yaakov Ariel, rav of Ramat Gan, has said that the alternate hechsher known as Hashgacha Pratit cannot be relied upon for kashrut. He also said about its founder, Rabbi Aaron Liebowitz, that not every rav can give kashrut certification, and definitely not someone who is destroying kashrut.

He also said that the various Badatz hechshers generally only go into a place and declare it kosher after the Rabbanut has already done so. The Badatz cannot be relied upon in a place where they declared it kosher without first the Rabbanut doing so, according to Rav Ariel.
source: Srugim

So, according to Rav Ariel, Hashgacha Pratit is just like any other hechsher - just like any private Badatz, for example. According to Rav Ariel, only the Rabbanut can give kashrut and be trusted, and no private hechsher can.

Legally that is the case, and will be so even more so after Shas's new law will be passed in the near future. Halachically that is not the case.

According to halacha all you need is to trust the person telling you it is kosher. There is no concept of hashgacha, private or public. I can trust the Badatz privately, without needing the Rabbanut, from a halachic perspective. I do not even need the Badatz if I trust the owner of the restaurant, or if he hires a private mashgiach that I trust.

That being said, as I have said before, I do not really get how Hashgacha Pratit works. At best it is like any other private hechsher, as Rav Ariel said, and one can choose to trust them or not. In reality though they are trying to do things differently. They have some system of volunteer supervisors, but for the most part people are relying on the word of restaurant owners who are largely not religious and whom they generally do not know personally. Can they be trusted? I don't know. Anybody and everybody can decide for himself or herself, but to me it seems spurious. Even though in theory I like the idea of going back to the system of trust that kashrut is really based on, I do not see how it can work the way it is working.

Someone asked Rav Yaakov Ariel, Chief Rabbi of Ramat Gan, if it is permissible to participate in the Tel Aviv Marathon that is fast approaching, considering it is a mixed-gender race. He also asked the same question about participating in Triathlons, events that include running, biking and swimming, that are mixed-gender races.

Rav Ariel's answer was simply, if people were dressed properly, it would be allowed. However, unfortunately, people are not dressed properly.
source: Yeshiva and NRG

uh oh. Good thing I am not participating in Marathon Tel Aviv...

Actually, this would apply not just to the Tel Aviv Marathon, but to all such marathons and sporting events. I know people who run a lot, but don't run marathons or other races only because of the way people (of the opposite gender) are dressed..

The truth is that this also applies to most of life - walking down the street, taking a bus, going to work, gooing to a mall, a supermarket - people are dressed immodestly everywhere. Granted, in sports clothes it is a lot of that concentrated into one place..

I find it interesting he did not employ the issue of it being a mixed-gender event, and only one of immodest dress.

Rabbi Yaakov Ariel, one of the leading Rabbis in Israel today and Chief Rabbi of Ramat Gan, has a problem with the way the recent hostage deal went down. He says that the government withholding information from the public as to the status of the soldiers, just so it can more easily pass the deal it was working on, is very serious deception. To put the citizens at risk so as to allow freedom to terrorists, most of whom will continue to be involved in terror is practically criminal.

If there was no knowledge as to their status then there is more reason to allow it, even when there is a certain risk to the public. After all, Karnit Goldwasser was facing a life of uncertainty and being an agunah - to release her from that burden, Rav Ariel says, the added element of risk is still worthwhile. However, if the government really knew the fate of her husband, she should have been told and she would not be an agunah, then the hostage trade would not have been necessary at the price it commanded.

To resolve this problem in future situations that should, chas v'shalom, arise, Rav Ariel has proposed we go back to the system King David used when sending soldiers out to battle. The soldiers of David would write a get and give it to their wife on condition that if they did not return from battle, they would retroactively be divorced. Then if the fate of the soldier would be unknown, she would not be an agunah, but would be a divorcee.

Rav Ariel has proposed that all soldiers going out to the front lines should give their wives the get of Dovid, or a get on condition, and that would resolve any future incidents and prevent wives from being agunahs.

So far his proposal has been rejected for reasons of possibly hurting morale. Yet Rav Ariel says that just as soldiers give fingerprints and DNA and other things "just in case" for identification purposes, when joining the army, so they can also give a get and it should not harm their morale.

I like the idea. I find great appeal in taking things from our history, biblical history, and finding ways to implement them as solutions today.