At the age of 32 I had to learn Hebrew from scratch. My starting point lay with my native Dutch and a couple of surrounding Western European languages. If you want to learn Hebrew by podcast you will find that the supply comes with English as a starting language and I will assume your starting point will be much the same as mine.
After some time, I did an 'Ulpan' (language class for immigrants in Israel) which is more intensive than podcast by a considerable magnitude. The reason I mention the Ulpan is that I found myself in class with as many as 20 nationalities and half of the students starting from English or another European language such as myself. For all of us, Hebrew was very outlandish and we struggled with much the same issues, although the situation for the native English speakers seemed most complicated. For them the differences and the complications seemed the most numerous.
That is bad news. The good news is though that the difficulties with Hebrew lie in the beginning of your learning curve. Picking up the alphabet, adapting to script from right to left, getting used to the pronunciation and to the odd root system of Hebrew words all hit you very hard from the get go. However then it turns out Hebrew is regular like mathematics. Grammar is as straightforward as it can be and the roots make a lot of sense after you have gotten used to them.
Real Hebrew therefore can be learned by the persistent who can take the initial barriers. Accept the baby steps at the start. Accept the seemingly useless verb exercises that skip the commons like to be and to have and force you to learn to conjugate verbs like to guard first. (I hated that) Podcasts can be a great help. Just do not forget to spend time on grammar and writing. Without that the token phrases will never make sense and remain sterile.
Hebrew - SurvivalPhrases (site, feed) - Very basic and not always faultless lessons.
Hebrew Podcasts (site, feed) - Basic podcast with phrases and grammar.
Learn Hebrew Pod (site, feed) - Basic podcast with phrases and grammar.
SBS Hebrew program (site, feed) - Australian radio in Hebrew. An excellent chance to hear living Hebrew. Fit for the more advanced learners.