I think it is difficult to get started as a chemist, which I suppose can be said about any entry-level job. I chose to be in the environmental chemistry field (so I can't say anything about pharmaceutical or other related areas). I had an internship at a water research center during my junior year and did a double-major in chemistry and math. When I was graduating in 2010 I was unable to land a job (though looking back now my job search wasn't nearly as extensive as it should have been).
I ended up going to graduate school to get an MS in environmental science, focus area environmental chemistry. I sent out about 50-60 job applications when I was nearing graduation, in my state and also 3-4 surrounding states. It seems like with the career prospects for recent chemistry grads you can't be too selective about where you want to live, which is one major drawback and is especially true if you don't have many connections, like me. If you live in a large city you might not have this problem, but I think in general this is more of a problem for people who choose chemistry compared to say accounting or computer programming.
My experience has been that employers do not pay much attention to the online applications. It's more useful to find contacts at the companies you are interested in and email them your resume directly. I had about a 5-10% response rate, and got two job interviews. The first was at a commercial environmental lab, and they did not hire me. The second was at a quality assurance company, and they hired me to do data validation, which essentially is reviewing lab data packages (usually thousands of pages per packet) to make sure their work is in accordance with EPA's requirements. I was making about $18 an hour there, in an area with a low cost of living.
It was a very repetitive job, but I was okay with it since I am a good worker and was hoping to be promoted. That outlook changed when the company lost their primary client (they had all their eggs in one basket for the most part), and laid off several people. The rest of us didn't have much work to do. It seems like overnight my job description went from "data validator" to "telemarketer" - They were expecting me to contact companies to see if they were interested in our services. I considered that a bad sign and started looking for jobs again.
I did not have much trouble getting hired at a nearby commercial environmental lab, for $20 an hour. It started out well, but I soon found out that the place is very poorly managed. As a result, they've had financial problems and had to do lay-offs as well as salary cuts. This resulted in people quitting and worsening the lab's reputation. The people they are able to find to work there are either incompetent or lazy (or both). I feel justified in saying this because over the past year I have had four different supervisors, one of whom was fired for data fraud. From what I have seen in online reviews of other environmental labs, conditions are only slightly better elsewhere. The take-home point of all this is that my personal experience has been that the environmental field is volatile, and lay-offs are common. I have only been working three years but have heard this from people with many years experience as well.
Another major downside to lab work is the chemical exposure, which varies depending on what you get into. When I started at the lab where I work now I was doing volatiles analysis exclusively. They now have me doing semi-volatiles extractions as well, which oddly enough involves much more chemical exposure than volatiles. It's not really something you think about when you're in school. For lab classes in school they're interested in minimizing waste since there are so many students who have to do the experiment, so experiments are designed on a smaller scale and chemical exposure is low. At a production lab, you can go through several 4-L bottles of solvent in a day, some of which are known carcinogens. At my current job, the fume hoods aren't in great working condition since they don't have the money to fix them.
Lastly, there isn't much room for creativity with analytical chemistry. Every once in a while I get a sample that is challenging to analyze, but for the most part the EPA tells you exactly how it has to be done. To get the R&D jobs for the most part you need a PhD. And I just read an article about PhD chemists having trouble landing jobs as well...
Those are the drawbacks. One major plus for working in a lab is that you get to be on your feet, instead of sitting at a computer all day. Another is that you don't have to deal with the public. Even at a small place like where I work now, there are project managers who are there to put up with customers' complaints. I actually am lucky enough to work alone.
I have stayed in the environmental field because I care about the environment and know that I do a good job (especially compared to the people who falsify data, which is apparently common in labs). With that being said, if I could go back and major in something else with better job prospects, I would. I know it is hard for any recent grad to find a job, but the majority of my classmates who majored in engineering fields are now engineers, undoubtedly making more money than me and doing more interesting work.