The poll's question: Can using logic lead to ilogical and erromeous results?
The question is terminally messy.
So, yes, using logic can lead to erroneous results.
For example if the premises are wrong.
Or if logic is applied wrongly. This happens, all the time.
However, still today we don't know whether logic has intrinsic flaws or not. It is not only plausible, but probable that logic works near perfection for a range of problems but not outside of this range. The reason for that is simple: logic is a capacity of the human mind and the human mind is the result of natural selection. As such, logic is most likely faultless for those problems which have been operational in natural selection but there is no apparent reason that it should also be faultless for problems that haven't been tested at all but also for problems too infrequent to have made a dent in the evolution of logic.
The basic principle of biological functions generally is that they are fundamentally compromises between several constraints and are therefore never optimal in respect to any one of these constraints. A better logic would likely have required a much larger brain, probably to the detriment of other functions.
So, on probability, our logic must have intrinsic flaws and therefore using logic is likely to lead to faulty conclusions for specific problems, in particular for complex problems.
This wouldn't affect ordinary life problems.
However, with the development of scientific theories that are of increasing complexity, it seems inevitable that we hit the wall of invalidity at some point in the future. Computers could come to provide an extension of our logic, providing we're able to understand the problem and design the solution to begin with.
Now, your question was in fact about formal logic, presumably current mathematical methods of formal logic...
Then the answer is, yes, absolutely, and inevitably, and in very concrete terms.
EB