We investigate constraints on some key cosmological parameters by confronting metastable dark energy models with different combinations of the most recent cosmological observations. Along with the standard $Lambda$CDM model, two phenomenological metastable dark energy models are considered: (romannumeral1) DE decays exponentially, (romannumeral2) DE decays into dark matter. We find that: (1) when considering the most recent supernovae and BAO data, and assuming a fiducial $Lambda$CDM model, the inconsistency in the estimated value of the $Omega_{rm{m,0}}h^2$ parameter obtained by either including or excluding Planck CMB data becomes very much substantial and points to a clear tension~citep{sahni2014model,zhao2017dynamical}; (2) although the two metastable dark energy models that we study provide greater flexibility in fitting the data, and they indeed fit the SNe Ia+BAO data substantially better than $Lambda$CDM, they are not able to alleviate this tension significantly when CMB data are included; (3) while local measurements of the Hubble constant are significantly higher relative to the estimated value of $H_0$ in our models (obtained by fitting to SNe Ia and BAO data), the situation seems to be rather complicated with hints of inconsistency among different observational data sets (CMB, SNe Ia+BAO and local $H_0$ measurements). Our results indicate that we might not be able to remove the current tensions among different cosmological observations by considering simple modifications of the standard model or by introducing minimal dark energy models. A complicated form of expansion history, different systematics in different data and/or a non-conventional model of the early Universe might be responsible for these tensions.
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