I was allowed to enter the airport terminal by showing a boarding pass for a future flight. Should I be concerned about "security"?

The reason why you have to show your boarding cards at the security check is not because it is insecure to let people without boarding passes in (there is no particular reason to think people without boarding cards are more dangerous than people with boarding cards), but merely to reduce the workload of the security screens.

If people without boarding cards were allowed through security, many friends and family of departing passengers might want to accompany them to the gate, making the checkpoint lines longer for everybody and potentially requiring more security screeners to be hired.

But it is not really security problem to let people without boarding cards through the check, given that they (you) were subjected to the same actual security screening for dangerous items as everyone else.

If you're concerned about that minor issue, you should really look into how the USA's Transportation Security Administration (TSA) failed 95% of security tests last year. A simple Google search for "TSA failure rate" will reveal dozens of articles on how airport security is nothing but mere theater. And yet it costs that country's taxpayers roughly US$7 billion per year.

An far more important reason than security concerns for having to present your boarding pass at the security line is to help channel passengers to their correct departure areas. They look at the boarding pass you present, and if it's one for the far other end of the airport direct you there rather than having you enter the wrong place and possibly hours later have to rush several kilometers to get to your actual gate.

As the vast majority of passengers won't have more than one boarding pass with them at any one time, your experience is just not one that is handled by this small extra bit of customer service.
In fact at Schiphol they have airport staff standing before the actual security lines directing you this way or that based on your boarding pass (just as they have people directing you to checkin lines based on your ticket).

Security checks need to be updated when they fail, so it does help if individuals who notice a possible fail inform the service that runs or controls them.

I noticed that in more places the boarding pass checks are done by machines and it is more likely for those to catch the wrong dates if the software is instructed to do so.
I think it is good to warn the security firms and the airports in case they have overlooked the option of using a still to come boarding pass. There are not that many companies that allow you to check in more than 30 hours ahead of time and it is likely that the date is not part of the checks now because of that. Most people will not have boarding passes for more than the current and the next day.

But on the other hand, I do not think your security was ever less than acceptable, if not 100%. It is not hard to buy an international ticket and get a boarding pass for any given day and unless you are suspected of being or becoming a terrorist nobody will worry about you having one.
The security person at the first checkpoint has no reason to be suspicious of people using a future time boarding pass. And you were not allowed on the flight with the wrong pass, so no harm done there as well.

Good security checks depend very much on detecting suspicious behaviour. If you have a valid boarding pass and by mistake go to the wrong gate, you will be behaving like someone who has a valid boarding pass and raise no suspicious. If you have a forged boarding pass and intentionally go to a gate where you shouldn't be, you may very will raise suspicion and be stopped. You can't judge security by their inability to stop innocent travellers that made some mistake.

As pointed out by others, boarding pass "checks" at security are usually not really there for security reasons. It's completely meaningless without also checking associated photo ID, and that's done at the gate.

As already stated by others, reasons for the "check" include avoiding non-passengers entering the secure area and making sure you enter the right terminal. When checked manually, the person doing the checks is usually concentrated on checking a single item on each boarding pass, usually the terminal or gate area, or the airline, nothing more.

Another reason for the "check" (but that usually involves a scan at each point, so it's probably not the case here) is to count waiting times. Someone will scan your boarding pass when you enter the queue, someone else will scan it once you actually get to the scanner. And the end result is displayed on pretty little screens.