Is there any halachic problem with singing or playing the song "haTikvah," considering that it was written by a secular Zionist and is the national anthem of the State of Israel?
HaTikva is the Israeli national anthem. Certainly, how one views the State of Israel will have bearing on how one views its national anthem.
HaTikva was written by a secular Jew, and it speaks of a Jewish dream "to be a free people in our land", omitting any religious language.
Some religious Zionists will thus sing HaTikva with the modification from "am chofshi" to "am kodshi", a holy (instead of free) nation.
Rabbi Abraham Isaac Kook, Chief Rabbi of what is now Israel, proposed a different anthem with more religious overtones. Yet as it didn't really catch on, he was not opposed to singing HaTikva.
I suppose the reasons one would find it halachically problematic to sing HaTikva would therefore have to be one (or more) of the following beliefs:
The question of #1 is far beyond the scope of mi.yodeya.
As for #2, Rav Kook and his followers didn't think so; I'm not sure the question can be "answered" any better than that.
And regarding #3, R' Moshe Feinstein was asked about songs that became very popular in the Orthodox world that were composed by someone less-than-Orthodox. He writes that if the composer was just a sinner and not a heretic, it would be no problem. If the composer was a heretic, then his music would be prohibited from "religious use", but playing music at a wedding isn't "religious use." It would be proper, however, for a Torah scholar to avoid it.
I think all would agree that singing HaTikva is not done as "religious use", so therefore not completely prohibited. The only quesion remaining is whether it's "preferably avoided by Torah scholars", and how to weigh that preference against the value of recognizing the anthem. So see #2.