Should I email a group regarding issues in work they've cited?

It would be fine to contact them and say that you tried X and would like their help figuring out why you did not get result Y.

Assuming you are right and they are wrong might be considered rude by some people.

Whether a researcher has an ethical obligation to act is field dependent: I know no field that requires a researcher to reveal their research beliefs; researchers are ethically free to keep their research private. (Perhaps with some exceptions which demand disclosure to the state. And some well-defined contexts, e.g., human experimentation, as noted in a comment.)

Researchers may feel they have a moral obligation to share. Email is appropriate for an informal, under-developed idea; a technical report for a more formal, better-developed idea; and a peer-reviewed publication is appropriate for formal, developed ideas. (Draft reports/submissions can be shared by email.)

When emailing peers, I recommend positing that your theory must be wrong, because it contradicts the work of peers, and that you must have made a mistake. You can then ask where you are mistaken, where you have misunderstood their results.

In seeking clarification, rather than raising concerns, surely no one can fault you.

Referring to @ZeroTheHero's answer ("an email alert from an undergraduate would instantly go in the trash and/or spam"); if you are working under the supervision of someone else, even nominally, it would be a good idea to run your issues by them first, for two reasons:

• you might be mistaken, a more senior person in your field might be able to confirm or disconfirm your results fairly easily;
• politically, it would be a good idea both to get a more senior person on your side (you might even ask them to make the first contact), and to avoid dragging someone who is supervising you into a potentially sticky political situation without their knowledge.