Eating high nitrate foods has made a nice difference for me. It has dropped my systolic blood pressure by about 10 points. I was getting quite a few readings that were 130-135/85-90, i.e. prehypertensive. Since I started eating lots - and I mean LOTS - of arugula, spinach, carrots and celery, my blood pressure is right at 120/80. And I make the argument in my link on How to Increase Your Nitric Oxide Naturally, that Mother Nature seems to have provided an alternate pathway for us to boost our nitric oxide levels with these high nitrate foods.
For a guy like myself who seems to have some amount of endothelial dysfunction from decades of a Western lifestyle, this is a huge help. Young guys, who normally have very low levels of arteriosclerosis, are able to pump out ample nitric oxide through the normal pathway of their artery walls, but that's often not the case for anyone 35+.
However, the question remains: is it SAFE to eat high nitrate foods? Is it safe for someone like myself to eat a lot of arugula and spinach and carrots? Okay, now that might seem like a foolish question at first, but the problem is this little equation:
Nitrates in Food + Amines in Food => Nitrosamines
Nitrosamines are compounds that have been implicated in many cancers. If you're a health reader, you'll see them come up from time to time in various discussions. For example, nitrosamines are suspected by many as being the primary carcinogen from smoking. And, from what I have seen, nitrosamines do not play any positive role and have the potential to cause cancer.
Fuel has been added to the argument from the fact that processed and possibly red meats have been implicated in certain cancers, such as of the colon. And, of course, the significance of that is that red and processed meats have nitrates and nitrites added to them:
"An elevated risk of colon cancer was associated with red meat intake...between high and low quintiles. Men who ate beef, pork, or lamb as a main dish five or more times per week had a relative risk of 3.57 compared to men eating these foods less than once per month. The association with red meat was not confounded appreciably by other dietary factors, physical activity, body mass, alcohol intake, cigarette smoking, or aspirin use." 
Nitrates added to meat and beer have been lowered over the years and so perhaps this risk has lessened. For example, notice the reductions that were achieved in German beer:
"The dietary exposure to NDMA and other volatile N-nitrosamines has been calculated in a number of food surverys...Reductions in the use of nitrates and nitrites used for curing meats and modifcation of malting techniques in the brewing industry have resulted in significant reductions in the levels of N-nitroso compounds over the last 5 years. In West Germany, the daily NDMA exposure from beer of 0.74 ug/day in 1979/1980 has been reduced to 0.1 ug/day in 1987." 
NOTE: NDMA is one of the most carcinogenic of the "naturally" occurring nitrosamines.
My point here is not to challenge eating meat, but rather to point out that the concern is very real and has been explored by a number of researchers. One author stated that "these data provide additional support for the hypothesis that nitrosamines are carcinogenic to the rectum in humans and that RM [Red Meat] and, in particular, PMs [Processed Meats] are significant sources of exposure for these compounds." 
A meat eater will often counter with the argument that if nitrates added to meat are carcinogenic, then the nitrates in high-nitrate plant foods are also likely carcinogenic as well. And so this leads to the all-important question:
"Can nitrates in plant foods increase nitrosamine formation and, therefore, cancer risks?"
First of all, I don't think anyone has a definitive answer. That said, I do think there is good evidence that plant-based nitrates do NOT cause cancer even though I cannot prove it. As always, though, I will caution you and say talk to your doctor and do your own research.
But let me explain why I don't think this is much of an issue:
1. Lack of Study Evidence. As far as I know, there is NO evidence that high nitrate plant foods cause cancer. Why are there numerous studies linking red and processed meats to increased colon cancer risks and none, for example, to spinach, lettuce, beets or other foods?
2. Spinach Probably Reduces Colon Cancer Risk. Spinach has been found to very likely REDUCE colon cancer risk, according to one study by the Linus Pauling Institute that found that "consumption of spinach can partially offset the damaging effects of the carcinogen. In tests with laboratory animals, it cut the incidence of colon tumors almost in half, from 58 percent to 32 percent."  Many other plants reduce nitrosamine formation and so this may be another reason that plant-based nitrates have not been shown to have any negative health effects.
3. Lack of Epidemiological Evidence. Every population study that I have seen that looks at vegetable consumption and/or vegetarian diets shows equal or improved cancer risks. Considering the fact that vegetarians eat a lot of greens and high nitrate foods, then why don't we see them with more cancer issues?
4. Questionable Increase in Nitrosamines. Consuming nitrates does not seem to raise nitrosamines in the urine to dangerous levels according to one (older) study. 
My guess is that plants have many compounds
a) that are so effective at decreasing cancer risk that they overwhelm any effects from nitrosamines, or
b) actually reduce the conversion of nitrates and amines into nitrosamines.
Again, I certainly do not know that definitely and this is my conclusion from examining #1 - #4 above.
However, let's say that you still feel like consuming large amounts of nitrates in plants is somewhat dangerous and you want to hedge your risks. Are there any solutions? Here are a couple of ideas:
1. Avoid Simultaneously Consuming Medium and High Amine Foods. A compromise solution is to avoid the other half of the equation, i.e. be careful not to eat medium or high amine foods at the same time you consume medium or high nitrate foods. There are many lists of amines in food out there, so I am not going to attempt to reproduce that. But, as an example, I would need to be careful about consuming tomatoes, sardines, almonds, peanuts and walnuts within a couple of hours of eating one of my higher nitrate meals.
2. Low Fat Diet + Vitamin C. Vitamin C can lower nitrosamine formation significantly. In fact, the Linus Pauling Institute reports:
"About 1970 it was discovered that ascorbic acid inhibits nitrosamine formation. Consequently, the addition of 550 ppm of ascorbic acid is now required in the manufacture of cured meat in the U.S. Actually, most cured meat manufacturers add erythorbic acid (an isomer of ascorbic acid) rather than ascorbic acid. Although erythorbic acid has reduced vitamin C activity, it is as effective as ascorbic acid in inhibiting nitrosamine formation and is also cheaper than vitamin C." 
However, one caution I have regarding this philosophy is that there is one study out there that shows that if you have low fat levels in your stomach and gut, you will get reduced nitrosamine formation from Vitamin C but if the presence of even medium amounts of fat, it can increase nitrosamine formation. To play it safe, you may want to eat lower fat combined with Vitamin C to make sure you get the full benefit.
1) http://legacy.library.ucsf.edu/documentStore/w/t/i/wti86b00/Swti86b00.pdf, "Carcinogenic N-nitrosamines in the diet : occurrence, formation, mechanisms and carcinogenic potential", German Cancer Research Center, Institute of Toxicology and Chemotherapy, Received 22 December 1989
2) Cancer Res, May 1 1994, 54:2390, "Intake of Fat, Meat, and Fiber in Relation to Risk of Colon Cancer in Men"
3) Cancer Epidemiol Biomarkers Prev October 2002 11; 1019, "Red Meat Intake, CYP2E1 Genetic Polymorphisms, and Colorectal Cancer Risk1"
5) IARC Scientific Pub, 1978(19):443-460, "The intake of nitrate, nitrite and volatile N-nitrosamines and the occurrence of volatile N-nitrosamines in human urine and veal calves."
7) Gut, 2007; 56:1678-1684, Published Online First: 4 September 2007, "Fat transforms ascorbic acid from inhibiting to promoting acid-catalysed N-nitrosation"