In some countries like Australia, Singapore etc, A candidate may be enrolled into Masters leading to PhD program on condition that he/she will pass the candidature test after the 1st year and are subsequently given PhD in the final/fourth year (subject to successful completion), which results in no M.Sc. degree in between.
Is there any discrepancy towards these PhD holder in academic or professional life?
No. Once you have a PhD, nobody cares about your previous degrees, or if you even graduated from high school.
(I know at least one tenured professor who did not graduate from high school.)
This answers the title question.
It is not a bad idea to take a break between a BSc and a PhD, just to see what else is out there in the world. Maybe do a bit of travel or work for six months or year. The disadvantage thus of doing a PhD right after a BSc is that you spend too much time in school, getting deeper and deeper into one topic, without taking an opportunity to broaden your perspective.
To amplify JeffE's answer, there are some instances where it will be inconvenient, in the sense that you will have to explain your situation.
Personally, I hold no master's degree. When I started my present job in Germany, this was looked upon as very unusual, and I had to explain that I attended a degree-granting university that did not require a master's for admission to PhD candidacy. (In Europe, the norm is that you essentially have to have a master's before beginning your PhD candidacy.)
Beyond that, however, there is generally no concerns beyond things that can be relatively easily explained. (The only thing I can think of is that if qualifications for a position are based on "years of experience," the truncated education may mean more post-educational work is required to satisfy the requirement.)
Mainly, the answer is no, if you have a PhD no one will care whether you have a master's degree in the same area or not.
However, I disagree with JeffE that no one will ever care about your previous degrees. This statement is nearly true with regard to research, but I think it may be false for some other areas. For example, if you want to teach at a liberal arts school (undergraduate-only, focused more on breadth than many schools), then you'll have a better chance to land such a job if you got your bachelor's degree at a school like that. At times I find it helpful to mention that I got a master's degree in optimization and algorithms, rather than just saying that I have a master's in math. I think this can more readily convey the particular skill set I acquired. If the people evaluating you always did so rationally and with due diligence, yours master's degree (or lack thereof) probably wouldn't matter. However, humans are often lazy and/or emotional, so your mileage may vary.
I don't have an MS, but I do have a BS and a PhD in the same field. I have had no professional problems as a result.
