Degenerate times are not without possibility, though; keeping vows during degenerate times, for example, is said to have a larger effect than keeping those same vows during less degenerate times. The prayers of (and to) the Medicine Buddhas are said to be particularly powerful during this degenerate age.
While alarmism takes place in every age, it's also true that languages, peoples and religions do actually wax and wane. Traditions as a whole, worldwide--herbal knowledge, survival knowledge, indigenous musical knowledge, linguistic knowledge--are without question waning today, rapidly. If one looks closely at Buddhism, the number of "deep" practitioners is, has without question plummeted in the last half century, as it has for deep practitioners of nearly every category of traditional knowledge.
There will likely be a great difference in the kind of Buddhism transmitted in more casual environments, compared to the kind of Buddhism transmitted from one deeply contemplative teacher to a new, deeply contemplative teacher who has followed the first teacher around for 20 years or so from youth. It doesn't necessarily mean doomsday, but given the emphasis Buddhism places on personal practice, especially for those planning to teach, I think it's important to think of these changes and what they mean. It could be that modern man will somehow find a way to continue to maintain a tradition of deep contemplation, but at the moment this aspect of Buddhism strikes me as endangered.
There's absolutely nothing wrong with lay Buddhism and those of us living our Buddhism day to day among our families; it's wonderful, completely. I just don't think we can honestly say that losing much of the tradition of devoted contemplative teachers is without effect.
The Irish language is undergoing a related process; mother-tongue speakers are dwindling rapidly, but second-language learners are increasing or least holding. There is a quantum difference, though, between a living, home language and a classroom language.
"Degenerate" isn't really a pejorative, just a descriptive. Looking around, I feel I see a lot of degeneration of traditional knowledge, so "degenerate times" seems accurate. I suppose the question is whether what we're replacing that knowledge with is equal in value.
Find teachings which are the correct medicine for you.
What was the moral character of the doctor/nurse who administered your smallpox vaccination as a child, or your latest round of antibiotics as an adult? Good medicine is not contaminated by those giving it. But we, the student, need to be sure to concentrate on the medicine and not get hung up on the personality of the one dispensing it.
Just a wee point of clarification that the Dalai Lama is not the head of the Gelug sect - that's the Ganden Tripa, which I believe currently is Thubten Nyima Lungtok Tenzin Norbu.
The sad thing in all of this is that the positive side is rarely talked about. There have always been differences of opinion in Buddhism, and always ways to deal with them and move on. No one issue is the be-all and end-all.