The Rabbanut has released a few recent incidents to show how important it is to make sure to eat and buy food only in places that have current certificates of kashrut.

I agree with that sentiment. It is my biggest problem with an organization like "Hashgacha Pratit" that largely (not entirely) relies on the trustworthiness of the proprietor of the establishment with some basic training. And especially with restaurants with no supervision at all except for perhaps a picture of a rabbi on the wall and the fellow behind the counter who assures you that it is all kosher. A lot of times, even without an actual attempt to deceive you, they just don't know and it would be an innocent mistake that you become the victim of.

3 stories:
1. the Rabbanut sent an inspector into an Asian restaurant with no teuda but stating that it is kosher. The fellow showed him an expired teuda from a vegetable supplier saying that this is where he buys stuff from. And that he only buys from kosher suppliers. I guess that teuda was an example of a kosher supplier he buys from.

Obviously that is no indication of kashrus for this restaurant. Maybe he also buys elsewhere?

The inspector relates that he spotted a container on the side that he decided to take a look at. It was a bottle of curry spice. Looking at the ingredients of this spice, the inspector discovered that it contains shrimp.

the proprietor admitted using the spice, not realizing what the problem was.

2. The Rabbanut sent inspectors to shops in the Carmel Market in Tel Aviv. They came upon a butcher that was selling meat with an ancient teudat kashrut - from the 1980s. The proprietor also brought out a certificate of lading that was also very old. Upon further inspection they discovered meat from a non-kosher meat factory in Um Al Fahm.

As the inspector points out, it is often the naive consumers, the traditional, who become the victims of these fraudulent sellers. The more religious know to look and check and ensure the kashrut level of the food, while the traditional just accept a statement of kashrut.

3. A wedding hall in Jerusalem billed as "mehadrin min hamehadrin" using private certification (a group called Ohr Eliyahu), was caught with refrigerated lamb meats that still had skin and hair on them.

The proprietor admitted that these meats had come from a private shechita performed in his own house. It seems he could not even say who had shechted and kashered the meat, if anyone actually did. You cannot kasher meat that still has the skin attached.
sources: Srugim and Kikar

The most important aspect of kashrut observance when eating out or buying food, is simply being aware and paying attention. It does not matter what hechsher you do or do not rely on - be aware of what you are looking at and pay attention to anything that looks suspicious, even if it has a reliable name on it or a fancy-looking logo.