MIN_CHANGE is a privacy leak, since it is an easily observable wallet behaviour. Any output almost equal, but minimally larger than MIN_CHANGE is highly likely the change output of a tx.

Also, MIN_CHANGE is quite high, considering the value of bitcoin.

An easy fix for the second issue would be to just lower the value, but maybe some randomization can be done to also fix the first issue?
{
    CMutableTransaction tx;
    tx.vout.resize(nInput + 1);
    tx.vout[nInput].nValue = nValue;
    tx.nLockTime = nextLockTime++;        
    COutput output(COutPoint(tx.GetHash(), nInput), tx.vout.at(nInput),  1,  -1,  true,  true,  true,  0,  false);
    OutputGroup group;
    group.Insert(output,  0,  0,  true);
    result.AddInput(group);
}
static void add_coin(const CAmount& nValue, int nInput, CoinSet& set, CAmount fee = 0, CAmount long_term_fee = 0)
{
    CMutableTransaction tx;
    tx.vout.resize(nInput + 1);
    tx.vout[nInput].nValue = nValue;
    tx.nLockTime = nextLockTime++;        
    COutput coin(COutPoint(tx.GetHash(), nInput), tx.vout.at(nInput),  1,  -1,  true,  true,  true,  0,  false);
    coin.effective_value = nValue - fee;
    coin.fee = fee;
    coin.long_term_fee = long_term_fee;
    set.insert(coin);
}
static void add_coin(std::vector<COutput>& coins, CWallet& wallet, const CAmount& nValue, int nAge = 6*24, bool fIsFromMe = false, int nInput=0, bool spendable = false)