Q:

Are calcium supplements harmful, even if you stay short of the maximum dose? 

Source: Do You Really Need Calcium Supplements?,  Margaret Polaneczky MD, 2014 Oct 2
You may also have heard that taking calcium supplements can lead to heart disease.  It’s still an open question.  Some studies suggest up to a 20% increase in heart disease in men and women who take calcium supplements, but other studies do not find this risk, or find it only in men and not women. 
My Recommendation
Unless you're at increased risk for a fracture (you can calculate your fracture risk here), forgo the supplements and get your calcium from food and drinks.  If you don't eat dairy, look to non-dairy calcium sources.  If you can't get your entire recommended daily allowance (RDA) of it from food, only take as much calcium supplementation as you need to make up the difference between dietary sources and the RDA for your age group. 

My teenage cousin doesn't suffer from any problems due to Calcium deficiency or that need Calcium supplementation.  He's lactose-intolerant. 
This article states that he needs 1000 mg of Calcium daily but it fails to address the impracticality of satisfying RDA from eating only  natural foods. 
Given his fear, he'll keep any consumption of Calcium supplements far below the maximum dosage.  Then are Calcium supplements safe to consume?   Conflicting answers from different doctors (whom he consulted) worsen his confusion.  Some recommend Calcium supplements, but others reject them. 
Footnote: I read the following which I list chronologically, but they sound uncertain:
Globe and Mail article
Science Based Medicine, this article and this one. 

A:

Background
In the past 10-15 years, thinking on calcium supplementation has shifted significantly.  In 2001, a National Institutes of Health (NIH) Consensus Development Panel on Osteoporosis made the recommendation that calcium should be supplemented to maintain daily intake 1000 - 1500 mg/day in older adults.  The reasoning behind this was that calcium is crucial for maintaining bone mass, which tends to deteriorate during the aging process, leaving this group at increased risk for fractures.  The panel acknowledged that most older adults do not obtain this amount of calcium from their diet; they therefore suggested supplementation to this level.  
Emerging Skepticism
Since the NIH recommendation in 2001, several large randomized controlled trials (RCTs) have called into question the efficacy of calcium supplementation to prevent fractures.  Although total fracture risk appears to be marginally reduced, the data suggested that hip fractures, which cause the most significant morbidity and mortality, are not prevented with calcium supplementation. 
Possible Risks
In addition to questions about efficacy, concerns have been raised about possible increase in cardiovascular events in those receiving calcium supplements, especially women.  In one RCT, postmenopauasal women were randomized to calcium supplementation or placebo.  The rate ratio of myocardial infarction was 1.67 in the calcium group compared to placebo.1 
Current State of Affairs  
In 2013 the US Preventive Services Task Force issued a statement recommending against calcium supplementation for primary prevention2 of fractures. 
Summary
Calcium supplementation has questionable efficacy for reducing clinically important fractures, and there is evidence to suggest that it may increase cardiovascular risk.  Because of these factors, large groups of smart people who spend their lives analyzing epidemiological data (read: the USPSTF) do not recommend calcium supplementation for primary prevention. 

Notes (a.k.a.  my shameless plug for epidemiology education)

1.  From such data we get headlines: Calcium increases the risk of heart attack by 167%!  When you see these things, have a look at the abstract with special attention to the confidence interval.  Here, the interval was 0.98-2.87.  Because it crosses 1, this is actually considered a not statistically significant result.  Although the trend is there, and similar results have been reproduced, this broad confidence interval at least warrants some caution when thinking about what the risk really is.  When interpreting data about rare outcomes, calculation of the Absolute Risk is also worthwhile for perspective. 

2.  Primary prevention refers to measures to avert an undesirable outcome in people with no history of a such a problem (here, fractures).  This stands in contrast to secondary prevention, which involves a population who has already experienced one incident where the goal is to prevent recurrence.  The latter group is expected to be at higher risk given their demonstrated propensity for the outcome.  For this reason, measures that incrementally decrease this risk tend to provide more absolute benefit compared to primary preventative measures.  This is based on the principle that absolute risk reduction depends on baseline risk, an important concept to understand when evaluating this literature. 

References

Bischoff-Ferrari, HA et al.  2007.  Calcium intake and hip fracture risk in men and women: a meta-analysis of prospective cohort studies and randomized controlled trials.  The American journal of clinical nutrition 86(6):1780–90. 

 
Bolland, MJ et al.  2008.  Vascular events in healthy older women receiving calcium supplementation: randomised controlled trial.  BMJ 336(7638):262–66. 

Moyer, V. A., U.S. Preventive Services Task Force.  Vitamin D and calcium supplementation to prevent fractures in adults: U.S. Preventive Services Task Force recommendation statement.  Annals of internal medicine 158(9):691–96. 

NIH Consensus Development Panel on Osteoporosis Prevention, Diagnosis, and Therapy.  2001.  Osteoporosis prevention, diagnosis, and therapy.  Pp.  785–95 in, vol.  285. 

Tang, BMP et al.  2007.  Use of calcium or calcium in combination with vitamin D supplementation to prevent fractures and bone loss in people aged 50 years and older: a meta-analysis.  Lancet 370(9588):657–66.